GCSE Maths: Distance-time graphs (Foundation)
Part of the GCSE Maths quadratic and other graphs chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Distance-time graphs
A distance-time graph shows a journey. Time goes along the horizontal axis and the distance from the start goes up the vertical axis. You can read how far someone has travelled at any time and when they reached any distance.
The important idea is that the gradient (steepness) of the line is the speed. Remember from Chapter 12 that gradient = change up ÷ change across. On this graph that is change in distance ÷ change in time, which is exactly the formula for speed.
- A straight sloping line means constant speed. The steeper it is, the faster the movement.
- A horizontal line means the distance is not changing: stopped (stationary).
- A line sloping down means the distance from the start is getting smaller: coming back.
Finding a speed. Pick a straight part. Work out the change in distance and the change in time, then divide. For the first hour: 15 km in 1 hour is 15 ÷ 1 = 15 km/h. For the last part: 20 km in 1 hour is 20 km/h.
Average speed. The average speed of a whole journey is total distance travelled ÷ total time taken. The time includes stops. For the cyclist: 35 km in 2.5 hours = 14 km/h.
Units. Distance in kilometres and time in hours give a speed in km/h. If the graph uses minutes, change to hours (divide minutes by 60) before you give a speed in km/h. 30 minutes = 0.5 hours.
Key ideas
- Gradient of a distance-time graph = speed = change in distance ÷ change in time.
- Steeper line = faster. Horizontal line = stopped. Line sloping down = returning.
- Average speed = total distance travelled ÷ total time taken (including stops).
- Use units that match: km and hours give km/h; m and seconds give m/s.
- Two journeys on the same graph meet where the lines cross.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Go up from the time to the graph, then across to the distance axis.
- Find the time on the horizontal axis. The horizontal axis shows time (Time (hours)).Find 2 on the bottom axis.
- Go straight up to the line, then straight across. Draw a vertical line up to the graph, then a horizontal line across to the vertical (distance) axis.The line meets the graph at height 25.
- Read the distance. Read the number on the distance axis, and include the unit.25 km
Check. This time is between 1.5 and 2.5, where the distance goes from 15 to 35; 25 lies between them. ✓
Watch out. Read from the right axis: time is along the bottom, distance is up the side.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (1.5, 15) to (2.5, 35)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 35 − 15 = 20 km
Change in time = 2.5 − 1.5 = 1 hours - Divide distance by time. Speed = distance ÷ time.20 ÷ 1 = 20 km/h
Check. Distance = speed × time = 20 × 1 = 20 km, the change we read from the graph. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (0, 0) to (20, 10)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 10 − 0 = 10 km
Change in time = 20 − 0 = 20 minutes - Divide distance by time. Speed = distance ÷ time.10 ÷ 20 = 0.5 km/min
- Change to the units asked for. The question wants a different unit, so convert.There are 60 minutes in an hour, so multiply by 60: 0.5 × 60 = 30 km/h
Speed = 30 km/h
Check. Distance = speed × time: 30 km/h for 20 minutes (after converting the units) gives 10 km. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Average speed = total distance ÷ total time. Change the time to hours so the answer is in km/h.
- Find the total distance travelled. Add the distances of the parts where the vehicle moved.10 + 30 = 40 km
- Find the total time taken, in hours. Speed in km/h needs the time in hours. There are 60 minutes in an hour, so divide the minutes by 60.60 minutes = 60 ÷ 60 = 1 hours
- Divide distance by time. Average speed = total distance ÷ total time.40 ÷ 1 = 40 km/h
Check. In 1 hours at 40 km/h the distance is 40 × 1 = 40 km. ✓
Watch out. Do not divide kilometres by minutes and call it km/h: convert the minutes to hours first.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. They meet where the two lines cross, because at that point they are at the same distance at the same time.
- Find the crossing point. Look for where the two lines meet.The lines cross at (2, 40).
- Read the time. The time is the horizontal coordinate.Time = 2 hours after Priya set off
- Read the distance. The distance from A is the vertical coordinate.Distance = 40 km
- Write the answer. They meet after 2 hours, 40 km from A.
Check. Priya: 20 km/h × 2 h = 40 km. Quinn has travelled 1 hour at 40 km/h = 40 km from B, which is 80 − 40 = 40 km from A. ✓
Watch out. The crossing point gives both the time and the distance.
Watch out
A horizontal line on a distance-time graph means the person is stopped, not moving at constant speed. A line sloping down means returning to the start, and the speed is still the size of the gradient. Also use total distance travelled ÷ total time for the average speed, and include the time spent stopped.Exam tip
When the graph is in minutes and the answer is in km/h, convert the time to hours first, or multiply a speed in km per minute by 60.Exercise 13G Distance-time graphs
Non-calculatorKey words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Go up from the time to the graph, then across to the distance axis.
- Find the time on the horizontal axis. The horizontal axis shows time (Time (hours)).Find 1 on the bottom axis.
- Go straight up to the line, then straight across. Draw a vertical line up to the graph, then a horizontal line across to the vertical (distance) axis.The line meets the graph at height 15.
- Read the distance. Read the number on the distance axis, and include the unit.15 km
Check. This time is between 0 and 1, where the distance goes from 0 to 15; 15 lies between them. ✓
Watch out. Read from the right axis: time is along the bottom, distance is up the side.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Go up from the time to the graph, then across to the distance axis.
- Find the time on the horizontal axis. The horizontal axis shows time (Time (hours)).Find 2 on the bottom axis.
- Go straight up to the line, then straight across. Draw a vertical line up to the graph, then a horizontal line across to the vertical (distance) axis.The line meets the graph at height 25.
- Read the distance. Read the number on the distance axis, and include the unit.25 km
Check. This time is between 1.5 and 2.5, where the distance goes from 15 to 35; 25 lies between them. ✓
Watch out. Read from the right axis: time is along the bottom, distance is up the side.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Go across from the distance to the graph, then down to the time axis.
- Find the distance on the vertical axis. The vertical axis shows distance.Find 35 km up the side.
- Go across to the line, then straight down. Draw a horizontal line across to the graph, then a vertical line down to the time axis.The line meets the graph at time 2.5.
- Read the time. Read the number on the time axis, and include the unit.2.5 hours
Check. Going the other way, the distance at that time is 35 km. ✓
Watch out. Read from the right axis: distance is up the side, time is along the bottom.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. A horizontal line shows a stop. Its length along the time axis is how long the stop lasts.
- Spot the flat part. A horizontal line means the distance is not changing, so the person is stationary (not moving).The line is flat from 1 to 1.5.
- Work out how long it lasts. Subtract the start time from the end time.1.5 − 1 = 0.5 hours
Check. The stop starts at 1 and ends at 1.5, so it lasts 0.5 hours. ✓
Watch out. A flat line does not mean "going at constant speed"; it means not moving at all.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (0, 0) to (1, 15)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 15 − 0 = 15 km
Change in time = 1 − 0 = 1 hours - Divide distance by time. Speed = distance ÷ time.15 ÷ 1 = 15 km/h
Check. Distance = speed × time = 15 × 1 = 15 km, the change we read from the graph. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (1.5, 15) to (2.5, 35)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 35 − 15 = 20 km
Change in time = 2.5 − 1.5 = 1 hours - Divide distance by time. Speed = distance ÷ time.20 ÷ 1 = 20 km/h
Check. Distance = speed × time = 20 × 1 = 20 km, the change we read from the graph. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Average speed = total distance travelled ÷ total time taken.
- Find the total distance travelled. Add the distance of every part where the person moved, in either direction (going back still counts as distance travelled).15 + 20 = 35 km
- Find the total time taken. Use the whole time from the start to the end, including any stops.2.5 − 0 = 2.5 hours
- Divide total distance by total time. Average speed = total distance ÷ total time.35 ÷ 2.5 = 14 km/h
Check. Distance = average speed × time = 14 × 2.5 = 35 km. ✓
Watch out. Include the time spent stopped. And do not average the speeds of the parts: use total distance ÷ total time.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. The greatest distance is the highest point of the graph.
- Find the highest point. It is at the top of the graph.The graph peaks at (2, 60).
- Read the distance. 60 km
Check. All other distances on the graph are less than 60 km. ✓
Watch out. Read the vertical axis.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. A horizontal line shows a stop. Its length along the time axis is how long the stop lasts.
- Spot the flat part. A horizontal line means the distance is not changing, so the person is stationary (not moving).The line is flat from 2 to 3.
- Work out how long it lasts. Subtract the start time from the end time.3 − 2 = 1 hour
Check. The stop starts at 2 and ends at 3, so it lasts 1 hour. ✓
Watch out. A flat line does not mean "going at constant speed"; it means not moving at all.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (0, 0) to (2, 60)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 60 − 0 = 60 km
Change in time = 2 − 0 = 2 hours - Divide distance by time. Speed = distance ÷ time.60 ÷ 2 = 30 km/h
Check. Distance = speed × time = 30 × 2 = 60 km, the change we read from the graph. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (3, 60) to (4, 0)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 0 − 60 = −60 km
Change in time = 4 − 3 = 1 hours - Divide distance by time. Speed = distance ÷ time.−60 ÷ 1 = −60 km/h
- Interpret the sign. The line goes down, so the distance from the start is getting smaller: the person is travelling back towards the start. The speed itself is the size of the gradient.Speed = 60 km/h (heading back)
Check. Distance = speed × time = 60 × 1 = 60 km, the change we read from the graph. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Average speed = total distance travelled ÷ total time taken.
- Find the total distance travelled. Add the distance of every part where the person moved, in either direction (going back still counts as distance travelled).60 + 60 = 120 km
- Find the total time taken. Use the whole time from the start to the end, including any stops.4 − 0 = 4 hours
- Divide total distance by total time. Average speed = total distance ÷ total time.120 ÷ 4 = 30 km/h
Check. Distance = average speed × time = 30 × 4 = 120 km. ✓
Watch out. Include the time spent stopped. And do not average the speeds of the parts: use total distance ÷ total time.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (0, 0) to (20, 10)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 10 − 0 = 10 km
Change in time = 20 − 0 = 20 minutes - Divide distance by time. Speed = distance ÷ time.10 ÷ 20 = 0.5 km/min
- Change to the units asked for. The question wants a different unit, so convert.There are 60 minutes in an hour, so multiply by 60: 0.5 × 60 = 30 km/h
Speed = 30 km/h
Check. Distance = speed × time: 30 km/h for 20 minutes (after converting the units) gives 10 km. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. A horizontal line shows a stop. Its length along the time axis is how long the stop lasts.
- Spot the flat part. A horizontal line means the distance is not changing, so the person is stationary (not moving).The line is flat from 20 to 30.
- Work out how long it lasts. Subtract the start time from the end time.30 − 20 = 10 minutes
Check. The stop starts at 20 and ends at 30, so it lasts 10 minutes. ✓
Watch out. A flat line does not mean "going at constant speed"; it means not moving at all.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (30, 10) to (60, 40)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 40 − 10 = 30 km
Change in time = 60 − 30 = 30 minutes - Divide distance by time. Speed = distance ÷ time.30 ÷ 30 = 1 km/min
- Change to the units asked for. The question wants a different unit, so convert.There are 60 minutes in an hour, so multiply by 60: 1 × 60 = 60 km/h
Speed = 60 km/h
Check. Distance = speed × time: 60 km/h for 30 minutes (after converting the units) gives 30 km. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Average speed = total distance ÷ total time. Change the time to hours so the answer is in km/h.
- Find the total distance travelled. Add the distances of the parts where the vehicle moved.10 + 30 = 40 km
- Find the total time taken, in hours. Speed in km/h needs the time in hours. There are 60 minutes in an hour, so divide the minutes by 60.60 minutes = 60 ÷ 60 = 1 hours
- Divide distance by time. Average speed = total distance ÷ total time.40 ÷ 1 = 40 km/h
Check. In 1 hours at 40 km/h the distance is 40 × 1 = 40 km. ✓
Watch out. Do not divide kilometres by minutes and call it km/h: convert the minutes to hours first.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (0, 0) to (10, 900)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 900 − 0 = 900 m
Change in time = 10 − 0 = 10 minutes - Divide distance by time. Speed = distance ÷ time.900 ÷ 10 = 90 m/min
Check. Distance = speed × time = 90 × 10 = 900 m, the change we read from the graph. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Speed is the gradient of a distance-time graph: speed = change in distance ÷ change in time.
- Pick the part of the graph. Speed is the gradient of the line. We need the change in distance and the change in time for this part.From (0, 0) to (10, 900)
- Find the change in distance and the change in time. Subtract the start values from the end values.Change in distance = 900 − 0 = 900 m
Change in time = 10 − 0 = 10 minutes - Divide distance by time. Speed = distance ÷ time.900 ÷ 10 = 90 m/min
- Change to the units asked for. The question wants a different unit, so convert.In one hour there are 60 minutes, and 1000 m = 1 km, so multiply by 60 then divide by 1000: 90 × 60 ÷ 1000 = 5.4 km/h
Speed = 5.4 km/h
Check. Distance = speed × time: 5.4 km/h for 10 minutes (after converting the units) gives 900 m. ✓
Watch out. Use the change in distance and the change in time for the same part of the journey, not the totals from the start.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Turn each part of the story into a straight line on the graph, then join the lines.
- Split the journey into stages. Each stage is a straight line on the graph, because each stage is at a steady speed (or stopped).Stage 1: 1 hour cycling 12 km. Stage 2: rest for half an hour. Stage 3: back home in 1.5 hours.
- Work out the coordinates (time, distance) at the end of each stage. Time goes along the bottom and distance goes up the side.(0, 0), (1, 12), (1.5, 12), (3, 0)
- Choose scales and draw the axes. Time goes up to 3 and distance up to 12. Label the axes with the quantities and units.x-axis: Time (hours). y-axis: Distance (km).
- Plot the points and join them with straight lines. Use a ruler. A flat line means stopped; a line going down means coming back towards the start.See the graph in the answer.
Check. Work out the gradient of each line: it gives the speed that the story describes. ✓
Watch out. A straight line between two points means constant speed.
Average speed 50 km/h
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Draw the graph from the story, then divide total distance by total time.
- Draw the graph. Plot (0, 0), (1.5, 90), (2, 90), (3, 150) and join with straight lines.Stages: 90 km, a stop, 60 km.
- Total distance. Add the distances travelled.90 + 60 = 150 km
- Total time. The stop counts as time taken.3 hours
- Divide. Average speed = total distance ÷ total time.150 ÷ 3 = 50 km/h
Check. 50 km/h for 3 hours gives 150 km. ✓
Watch out. Include the 30-minute stop in the total time.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. They meet where the lines cross.
- Find the crossing point. Look for where the lines meet.(2, 40)
- Read the time. The horizontal coordinate.2 hours after Priya leaves
Check. At t = 2 both are at 40 km from A. ✓
Watch out. Time is horizontal.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. They meet where the lines cross.
- Find the crossing point. (2, 40)
- Read the distance. The vertical coordinate.40 km from A
Check. Priya: 20 × 2 = 40. ✓
Watch out. Distance is vertical.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. The steeper line is faster. Compare gradients.
- Priya's speed. 80 km in 4 hours.80 ÷ 4 = 20 km/h
- Quinn's speed. 80 km in 2 hours (from 1 to 3 hours).80 ÷ 2 = 40 km/h
- Compare. Quinn is faster (40 km/h > 20 km/h); his line is steeper.
Check. Quinn's line goes down 80 in 2, steeper than Priya's 80 in 4. ✓
Watch out. Steeper = faster.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Think about what a horizontal line shows about the distance as time passes.
- Look at a horizontal line. As time goes on (moving right) the distance stays at the same height.The distance is not changing
- Link to speed. Speed = change in distance ÷ time. The change in distance is 0.Speed = 0 ÷ time = 0
- Conclude. The speed is 0: the person is stationary.Horizontal means stopped. Constant speed is a straight sloping line.
Check. In the car journey the flat part is the stop at the shop: the distance stays at 60 km for 1 hour. ✓
Watch out. Flat means not moving.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. A straight line has a constant gradient, so the speed is constant. Think about what a downward slope means.
- Look at the line. It is a straight line, so the gradient (speed) is the same all the way.Constant speed
- Work out the speed. The distance falls by 60 km in 1 hour.60 ÷ 1 = 60 km/h
- Explain the downward slope. It means the distance from the start is getting smaller: the car is travelling back towards the start.Not slowing down: returning at 60 km/h.
Check. A car that slows down would show a line that gets less steep (a curve). ✓
Watch out. A downward slope means returning, not slowing.
Key words. A distance-time graph shows how far something has travelled from its start (up the side) as time passes (along the bottom). The gradient (steepness) of the line is the speed, because gradient = change up ÷ change across = distance ÷ time. A flat line means stationary (not moving).
Method. Work out each runner's finishing time, then compare. Draw each as a straight line.
- Amy's time. Time = distance ÷ speed.200 ÷ 8 = 25 seconds
- Ben's running time. He runs 200 m at 10 m/s.200 ÷ 10 = 20 seconds
- Ben's finishing time on the clock. He started 4 seconds late, so add 4.4 + 20 = 24 seconds
- Draw. Amy: line from (0, 0) to (25, 200). Ben: line from (4, 0) to (24, 200).Ben's line is steeper and ends first.
- Compare. 24 is less than 25.Ben wins by 1 second.
Check. At 24 s Amy has run 8 × 24 = 192 m, 8 m short of the finish while Ben is at 200 m. ✓
Watch out. Remember to add the late start to Ben's time.