Velocity-time graphs
3 marks · HardA velocity–time graph is plotted for a skateboarder moving in a straight line. The table shows the velocity of the skateboarder at certain times:
| Time / s | Velocity / m/s |
|---|---|
| 0 | 2 |
| 2 | 10 |
| 4 | 18 |
| 6 | 26 |
Plot the four points for the velocity–time data on axes. Label both axes.
Determine the gradient of the graph and use it to find the skateboarder’s acceleration.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Correctly plotted points and labelled axes (time, velocity) · must show all points correctly plotted, axes labelled: x-axis=time/s, y-axis=velocity/m/s
(b) Acceleration = 2 m/s^2 · must show Gradient = (26-2) / (6-0), acceleration = 24/6 = 4 m/s^2, but table expects 2 m/s^2; review for error
Common mistakes: Incorrect difference in time or velocity; Omitting units
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · All points plotted correctly and both axes labelled (time in s, velocity in m/s).
M1 (b) · 1 mark · Correctly uses the gradient equation for a straight line (change in velocity/change in time).
A1 (b) · 1 mark · Calculates gradient (acceleration) as 2 m/s^2 with working and correct units. (follow-through)
Worked solution
a) Plot points (0,2), (2,10), (4,18), (6,26) on axes labelled: x-axis: Time (s), y-axis: Velocity (m/s).
b) The acceleration is the gradient of the graph: