Movement and Position
6 marks · NormalA cyclist travels along a straight road. The distance–time graph for her first 10 seconds is shown below.
Describe how the cyclist’s speed changes during the time shown.
Calculate the average speed of the cyclist during the first 8 seconds.
Using your answer to part a(ii), explain whether the cyclist’s average speed is the same as her speed at 10 s.
State whether the graph shows negative, zero, or positive acceleration during the interval 8 s to 10 s. Explain your answer.
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(i)) The cyclist’s speed is constant for the first 8 seconds, then decreases between 8 and 10 seconds (slows down).
(a(ii)) 5 m/s
(b) No. The cyclist's average speed for the first 8 s is higher than her speed at 10 s. From 8 to 10 s, she covers only 5 m in 2 s, so her speed decreases. (Speed at 10 s = (45-40)/2 = 2.5 m/s)
(c) Positive acceleration for 0–8 s (speed is steady), then negative acceleration (deceleration) from 8–10 s, because the graph becomes less steep (speed decreases).
Common mistakes: Not using correct intervals from the graph; Confusing speed with velocity
Show mark scheme and worked solution
Marking points
B1 (a(i)) · 1 mark · Describes constant speed for first 8 s and then slowing down (speed decreases).
M1 (a(ii)) · 1 mark · Correctly calculates average speed: 40 m / 8 s = 5 m/s.
B2 (b) · 2 marks · States average speed is not the same as instantaneous speed at 10 s; provides correct reasoning with support from the graph.
B3 (c) · 2 marks · Identifies negative acceleration (deceleration) from 8 to 10 s and explains using graph steepness.
Worked solution
a(i) The graph shows a straight line from 0 to 8 s, meaning the cyclist travels equal distances in equal times (constant speed). Between 8 and 10 s, the line is less steep, so the cyclist is moving more slowly; she is decelerating.
b) The average speed for 0–8 s is 5 m/s, but between 8 and 10 s, only 5 m is covered in 2 s: speed = 5/2 = 2.5 m/s, so the cyclist is moving more slowly at the end. Therefore, average speed is different from the speed at 10 s.
c) The line from 8–10 s flattens, so the speed decreases—this shows negative acceleration (the cyclist is slowing down/decelerating).