Forces and Motion
6 marks · NormalTwo students investigate the motion of a toy car by rolling it down a slope. The distance travelled after release is recorded at several times. Their data is given below.
| Time/s | Distance/m |
|---|---|
| 0.0 | 0.00 |
| 0.5 | 0.18 |
| 1.0 | 0.52 |
| 1.5 | 0.98 |
| 2.0 | 1.60 |
| 2.5 | 2.30 |
Plot a distance–time graph for the toy car using the data above. Label the axes with units.
Use your graph to estimate the average speed of the car between t = 0 and t = 2.5 s. Show your working.
Describe how you can tell from the graph whether the car was accelerating.
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) Graph: Distance (m) against Time (s). Points: (0,0), (0.5,0.18), (1.0,0.52), (1.5,0.98), (2.0,1.60), (2.5,2.30). · must show axes correctly labelled, points correctly plotted
(b) 0.92 m/s · must show uses speed = distance/time, correct substitution from table, accept 0.91–0.93 m/s
(c) If the graph is a curve getting steeper, the car is accelerating (distance increases more in each time interval). A straight line would mean constant speed. · must show refers to graph shape (curve/straight), explains meaning in terms of acceleration
Must show: Axes: Time (s), Distance (m), Data points plotted correctly, Curve shape for acceleration
Show mark scheme and worked solution
Marking points
P1 (a) · 1 mark · Axes correctly labelled with units.
P2 (a) · 1 mark · Points correctly plotted; graph shape matches data.
M1 (b) · 1 mark · Uses speed = distance/time with correct values from the data.
A1 (b) · 1 mark · Correct calculation of speed: (2.30 m / 2.5 s = 0.92 m/s, to 2 decimals).
B1 (c) · 1 mark · Recognises a curve indicates increasing speed (acceleration).
B2 (c) · 1 mark · Explains a straight line means constant speed, curve means acceleration.
Worked solution
a) On squared paper, plot Time (s) on the x-axis and Distance (m) on the y-axis. Plot the points from the table.
b) Average speed = total distance / total time = 2.30 m / 2.5 s = 0.92 m/s.
c) The graph is a curve that gets steeper with time, which shows acceleration – the car travels further each 0.5 s. If the car moved at constant speed, the graph would be a straight line.