GCSE Maths: Speed-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)
Speed-time graphs
A speed-time graph (also called a velocity-time graph) shows how the speed of something changes. Time is along the horizontal axis and speed is up the vertical axis. This is different from a distance-time graph, so be careful to read the labels on the axes.
- A line sloping up means the speed is increasing: accelerating.
- A horizontal line means constant speed.
- A line sloping down means the speed is decreasing: decelerating (slowing down).
The gradient of a speed-time graph is the acceleration: change in speed ÷ change in time. With speed in m/s and time in s the unit is m/s² (metres per second per second). A gradient of 2 means the speed rises by 2 m/s every second. A negative gradient means the speed is falling. This is a deceleration.
The area under the graph (between the line and the time axis) is the distance travelled. This works because distance = speed × time: speed is the height and time is the width. Split the area into rectangles, triangles and trapezia. (Chapter 25 returns to areas under curved graphs.)
Key ideas
- Speed-time graph: gradient = acceleration = change in speed ÷ change in time (unit m/s²).
- Sloping up = accelerating. Flat = constant speed. Sloping down = decelerating (negative acceleration).
- Area under the graph = distance travelled. Use a rectangle (flat), a triangle (starts or ends at 0) or a trapezium (area = ½(a + b) × width).
- Average speed = total distance ÷ total time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Go up from the time to the line, then across to the speed axis.
- Find the time on the horizontal axis. The horizontal axis shows time in seconds.Find 4 s along the bottom.
- Go straight up to the line, then straight across. The vertical axis shows speed.The line is at height 8.
- Read the speed. Write the unit.8 m/s
Check. The speed at this time is between the speeds at the two corners either side of it. ✓
Watch out. Read the vertical axis for speed.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (0, 0) to (8, 16)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 16 − 0 = 16 m/s
Change in time = 8 − 0 = 8 s - Divide. Acceleration = change in speed ÷ change in time.16 ÷ 8 = 2
- Write the answer with its unit. The unit is metres per second per second, written m/s².Acceleration = 2 m/s²
Check. The speed changes by 2 m/s every second, for 8 s: 2 × 8 = 16 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (18, 16) to (22, 0)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 0 − 16 = −16 m/s
Change in time = 22 − 18 = 4 s - Divide. Acceleration = change in speed ÷ change in time.−16 ÷ 4 = −4
- Interpret the sign. The line slopes downwards, so the speed is falling. This is a deceleration. As a gradient it is negative.Acceleration = −4 m/s² (a deceleration of 4 m/s²)
Check. The speed changes by −4 m/s every second, for 4 s: −4 × 4 = −16 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Distance travelled = area under the speed-time graph. Split it into rectangles, triangles and trapezia.
- Remember: distance is the area under the graph. Distance = speed × time. On the graph, speed is the height and time is the width, so distance is the area between the line and the time axis.
- Split the area into simple shapes. Use a rectangle where the line is flat, a triangle where it starts or ends at 0, and a trapezium otherwise.From 0 s to 8 s, a triangle: ½ × 8 × 16 = 64
From 8 s to 18 s, a rectangle: 16 × 10 = 160
From 18 s to 22 s, a triangle: ½ × 4 × 16 = 32 - Add the areas. The total area is the total distance travelled.64 + 160 + 32 = 256 m
Check. Sense check: the vehicle never goes faster than 16 m/s and travels for 22 s, so the distance must be less than 352 m. Our 256 m is smaller. ✓
Watch out. The unit of the area is the unit of distance (m), not m/s. Area = height × width means speed × time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Average speed = total distance ÷ total time. Find the distance from the area under the graph.
- Find the area of each part. Triangle, rectangle, triangle.Triangle: ½ × 10 × 20 = 100
Rectangle: 20 × 20 = 400
Triangle: ½ × 10 × 20 = 100 - Add to get the total distance. 100 + 400 + 100 = 600 m
- Divide by the total time. The time is 40 seconds.600 ÷ 40 = 15 m/s
Check. 15 m/s for 40 s = 600 m. ✓
Watch out. Average speed is not the top speed (20 m/s).
Watch out
On a speed-time graph a flat line means constant speed (not stopped). A line sloping down means slowing down, not going backwards. And a gradient is acceleration here, not speed. The area under the graph has units of distance (m), not m/s.Exam tip
Label each area you use (A, B, C) with its shape and its calculation, and add them at the end. Check the units of every axis before you start.Exercise 13H Speed-time graphs
Non-calculatorKey words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Go up from the time to the line, then across to the speed axis.
- Find the time on the horizontal axis. The horizontal axis shows time in seconds.Find 4 s along the bottom.
- Go straight up to the line, then straight across. The vertical axis shows speed.The line is at height 8.
- Read the speed. Write the unit.8 m/s
Check. The speed at this time is between the speeds at the two corners either side of it. ✓
Watch out. Read the vertical axis for speed.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. A horizontal line shows constant speed.
- Find the flat part. The line is flat from 8 s to 18 s.
- Subtract. End time minus start time.18 − 8 = 10 seconds
Check. The flat part is at 16 m/s for 10 s. ✓
Watch out. Flat = constant speed.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (0, 0) to (8, 16)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 16 − 0 = 16 m/s
Change in time = 8 − 0 = 8 s - Divide. Acceleration = change in speed ÷ change in time.16 ÷ 8 = 2
- Write the answer with its unit. The unit is metres per second per second, written m/s².Acceleration = 2 m/s²
Check. The speed changes by 2 m/s every second, for 8 s: 2 × 8 = 16 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (18, 16) to (22, 0)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 0 − 16 = −16 m/s
Change in time = 22 − 18 = 4 s - Divide. Acceleration = change in speed ÷ change in time.−16 ÷ 4 = −4
- Interpret the sign. The line slopes downwards, so the speed is falling. This is a deceleration. As a gradient it is negative.Acceleration = −4 m/s² (a deceleration of 4 m/s²)
Check. The speed changes by −4 m/s every second, for 4 s: −4 × 4 = −16 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (0, 0) to (10, 20)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 20 − 0 = 20 m/s
Change in time = 10 − 0 = 10 s - Divide. Acceleration = change in speed ÷ change in time.20 ÷ 10 = 2
- Write the answer with its unit. The unit is metres per second per second, written m/s².Acceleration = 2 m/s²
Check. The speed changes by 2 m/s every second, for 10 s: 2 × 10 = 20 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. A flat line shows the steady speed.
- Find the flat part. The line is flat between 10 s and 30 s.
- Read its height. The height is the speed.20 m/s
Check. Speed is read from the vertical axis. ✓
Watch out. Read the vertical axis for speed.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. The slowing-down part is the last sloping-down line.
- Find its start and end. It starts at 30 s and ends at 40 s.
- Subtract. 40 − 30 = 10 seconds
Check. The line reaches speed 0 at 40 s. ✓
Watch out. The end time minus the start time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (30, 20) to (40, 0)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 0 − 20 = −20 m/s
Change in time = 40 − 30 = 10 s - Divide. Acceleration = change in speed ÷ change in time.−20 ÷ 10 = −2
- Interpret the sign. The line slopes downwards, so the speed is falling. This is a deceleration. As a gradient it is negative.Acceleration = −2 m/s² (a deceleration of 2 m/s²)
Check. The speed changes by −2 m/s every second, for 10 s: −2 × 10 = −20 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Distance travelled = area under the speed-time graph. Split it into rectangles, triangles and trapezia.
- Remember: distance is the area under the graph. Distance = speed × time. On the graph, speed is the height and time is the width, so distance is the area between the line and the time axis.
- Split the area into simple shapes. Use a rectangle where the line is flat, a triangle where it starts or ends at 0, and a trapezium otherwise.From 0 s to 8 s, a triangle: ½ × 8 × 16 = 64
- Add the areas. The total area is the total distance travelled.64 = 64 m
Check. Sense check: the vehicle never goes faster than 16 m/s and travels for 8 s, so the distance must be less than 128 m. Our 64 m is smaller. ✓
Watch out. The unit of the area is the unit of distance (m), not m/s. Area = height × width means speed × time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Distance travelled = area under the speed-time graph. Split it into rectangles, triangles and trapezia.
- Remember: distance is the area under the graph. Distance = speed × time. On the graph, speed is the height and time is the width, so distance is the area between the line and the time axis.
- Split the area into simple shapes. Use a rectangle where the line is flat, a triangle where it starts or ends at 0, and a trapezium otherwise.From 8 s to 18 s, a rectangle: 16 × 10 = 160
- Add the areas. The total area is the total distance travelled.160 = 160 m
Check. Sense check: the vehicle never goes faster than 16 m/s and travels for 10 s, so the distance must be less than 160 m. Our 160 m is smaller. ✓
Watch out. The unit of the area is the unit of distance (m), not m/s. Area = height × width means speed × time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Distance travelled = area under the speed-time graph. Split it into rectangles, triangles and trapezia.
- Remember: distance is the area under the graph. Distance = speed × time. On the graph, speed is the height and time is the width, so distance is the area between the line and the time axis.
- Split the area into simple shapes. Use a rectangle where the line is flat, a triangle where it starts or ends at 0, and a trapezium otherwise.From 0 s to 8 s, a triangle: ½ × 8 × 16 = 64
From 8 s to 18 s, a rectangle: 16 × 10 = 160
From 18 s to 22 s, a triangle: ½ × 4 × 16 = 32 - Add the areas. The total area is the total distance travelled.64 + 160 + 32 = 256 m
Check. Sense check: the vehicle never goes faster than 16 m/s and travels for 22 s, so the distance must be less than 352 m. Our 256 m is smaller. ✓
Watch out. The unit of the area is the unit of distance (m), not m/s. Area = height × width means speed × time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Distance travelled = area under the speed-time graph. Split it into rectangles, triangles and trapezia.
- Remember: distance is the area under the graph. Distance = speed × time. On the graph, speed is the height and time is the width, so distance is the area between the line and the time axis.
- Split the area into simple shapes. Use a rectangle where the line is flat, a triangle where it starts or ends at 0, and a trapezium otherwise.From 0 s to 10 s, a triangle: ½ × 10 × 20 = 100
From 10 s to 30 s, a rectangle: 20 × 20 = 400
From 30 s to 40 s, a triangle: ½ × 10 × 20 = 100 - Add the areas. The total area is the total distance travelled.100 + 400 + 100 = 600 m
Check. Sense check: the vehicle never goes faster than 20 m/s and travels for 40 s, so the distance must be less than 800 m. Our 600 m is smaller. ✓
Watch out. The unit of the area is the unit of distance (m), not m/s. Area = height × width means speed × time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (0, 2) to (6, 14)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 14 − 2 = 12 m/s
Change in time = 6 − 0 = 6 s - Divide. Acceleration = change in speed ÷ change in time.12 ÷ 6 = 2
- Write the answer with its unit. The unit is metres per second per second, written m/s².Acceleration = 2 m/s²
Check. The speed changes by 2 m/s every second, for 6 s: 2 × 6 = 12 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Distance travelled = area under the speed-time graph. Split it into rectangles, triangles and trapezia.
- Remember: distance is the area under the graph. Distance = speed × time. On the graph, speed is the height and time is the width, so distance is the area between the line and the time axis.
- Split the area into simple shapes. Use a rectangle where the line is flat, a triangle where it starts or ends at 0, and a trapezium otherwise.From 0 s to 6 s, a trapezium: ½ (2 + 14) × 6 = 48
From 6 s to 10 s, a rectangle: 14 × 4 = 56 - Add the areas. The total area is the total distance travelled.48 + 56 = 104 m
Check. Sense check: the vehicle never goes faster than 14 m/s and travels for 10 s, so the distance must be less than 140 m. Our 104 m is smaller. ✓
Watch out. The unit of the area is the unit of distance (m), not m/s. Area = height × width means speed × time.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Read the height of the flat part.
- Find the flat part. The line is flat from 0 s to 6 s.
- Read the height. 12 m/s
Check. At 0 s the graph starts at 12 on the speed axis. ✓
Watch out. Speed is the vertical axis.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Acceleration is the gradient of a speed-time graph: change in speed ÷ change in time.
- Pick the part of the graph. Acceleration is the gradient of the line, so we use the change in speed and the change in time.From (6, 12) to (10, 0)
- Find the change in speed and the change in time. Subtract the start values from the end values.Change in speed = 0 − 12 = −12 m/s
Change in time = 10 − 6 = 4 s - Divide. Acceleration = change in speed ÷ change in time.−12 ÷ 4 = −3
- Interpret the sign. The line slopes downwards, so the speed is falling. This is a deceleration. As a gradient it is negative.Acceleration = −3 m/s² (a deceleration of 3 m/s²)
Check. The speed changes by −3 m/s every second, for 4 s: −3 × 4 = −12 m/s, the change we found. ✓
Watch out. Acceleration is the gradient. The height of the line is the speed, not the acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Distance travelled = area under the speed-time graph. Split it into rectangles, triangles and trapezia.
- Remember: distance is the area under the graph. Distance = speed × time. On the graph, speed is the height and time is the width, so distance is the area between the line and the time axis.
- Split the area into simple shapes. Use a rectangle where the line is flat, a triangle where it starts or ends at 0, and a trapezium otherwise.From 0 s to 6 s, a rectangle: 12 × 6 = 72
From 6 s to 10 s, a triangle: ½ × 4 × 12 = 24 - Add the areas. The total area is the total distance travelled.72 + 24 = 96 m
Check. Sense check: the vehicle never goes faster than 12 m/s and travels for 10 s, so the distance must be less than 120 m. Our 96 m is smaller. ✓
Watch out. The unit of the area is the unit of distance (m), not m/s. Area = height × width means speed × time.
Total distance 180 m
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Draw the graph from the story, then find the area under it.
- Draw the graph. Plot (0, 0), (6, 12), (16, 12), (20, 0) and join with straight lines.Triangle, rectangle, triangle.
- Find the areas. Use ½ × base × height for triangles and base × height for the rectangle.½ × 6 × 12 = 36
10 × 12 = 120
½ × 4 × 12 = 24 - Add. The total area is the distance.36 + 120 + 24 = 180 m
Check. Average speed 180 ÷ 20 = 9 m/s, which is less than the top speed 12 m/s. ✓
Watch out. Do not forget the two triangles at the ends.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Average speed = total distance ÷ total time.
- Find the total distance. Add the areas under the graph.100 + 400 + 100 = 600 m
- Divide by the total time. The time is 40 seconds.600 ÷ 40 = 15 m/s
Check. 15 × 40 = 600 m. ✓
Watch out. Average speed is less than the top speed.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. First find the time to reach 15 m/s (use the acceleration), then find the area of the triangle up to that time.
- Find the acceleration. Gradient of the first part.20 ÷ 10 = 2 m/s²
- Time to reach 15 m/s. Divide the speed by the acceleration.15 ÷ 2 = 7.5 seconds
- Area of the triangle. Base 7.5 s, height 15 m/s.½ × 7.5 × 15 = 56.25 m
Check. Average speed over this time is (0 + 15) ÷ 2 = 7.5 m/s; 7.5 × 7.5 = 56.25. ✓
Watch out. The triangle's height is the speed 15, not 20.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Think about what the height of the line shows.
- What does the height show? On a speed-time graph the height is the speed.
- What does a downward slope show? The speed is getting smaller.The car is slowing down
- Conclude. The car is still moving forwards while its speed is above 0. It stops when the line reaches the time axis.Slowing down (decelerating), not reversing.
Check. In the car graph the line falls from 16 m/s to 0 m/s over 4 seconds, a deceleration of 4 m/s². ✓
Watch out. Distance-time graphs go down when returning; speed-time graphs go down when 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. Think about the vertical axis: distance.
- Distance does not change. As time passes the line stays at the same height.
- Conclude. Speed = 0.Stopped
Check. Gradient 0 = speed 0. ✓
Watch out. Flat on a distance-time graph means stopped.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Think about the vertical axis: speed.
- Speed does not change. As time passes the line stays at the same height.
- Conclude. The speed is constant but not zero (unless the line is on the axis).Constant speed
Check. Gradient 0 = acceleration 0. ✓
Watch out. Check the axis labels.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Think about the vertical axis: speed.
- Speed increases. The line rises as time passes.
- Conclude. The gradient is positive, so the acceleration is positive.Accelerating
Check. The gradient is the acceleration. ✓
Watch out. On a speed-time graph the gradient is acceleration.
Key words. A speed-time graph shows the speed (up the side) as time passes (along the bottom). The gradient is the acceleration (how fast the speed changes), and the area under the graph is the distance travelled. Negative acceleration (the speed is dropping) is called deceleration.
Method. Compare the areas under the two lines for 20 seconds.
- Car A: speed at 10 s. Acceleration 2 for 10 s.2 × 10 = 20 m/s
- Car A: distance. Triangle for 10 s, then a rectangle for 10 s at 20 m/s.½ × 10 × 20 = 100 and 10 × 20 = 200: total 300 m
- Car B: distance. One triangle: base 20 s, height 20 m/s.½ × 20 × 20 = 200 m
- Compare. 300 − 200 = 100 m: Car A is further.
Check. Car A is always at a higher speed than car B for 0 < t < 20, so it must have gone further. ✓
Watch out. Compare areas, not final speeds (both finish at 20 m/s).