A sprinter runs a race of 200 m. His total time for running the race is 20 s. He starts from rest and accelerates uniformly for 6 s, reaching a speed of 12 m s¯¹. He maintains this speed for the next 10 s, before decelerating uniformly to cross the finishing line with speed V m s¯¹.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [M1] Use constant acceleration equations or find area in (t,v) graph to find the distance s₁ travelled in the first 6 seconds
2. [M1] Use constant acceleration equations or find area in (t,v) graph to find s₂ the distance travelled between 6s and 16s
3. [A1] Distance for first 16s is 36 + 10 × 12 = 156
4. [B1] Curve concave up for 0 < t <6 starting at (0, 0) ending at (6, 36)
5. [B1] Line, positive gradient, 6 < t < 16 starts at (6, 36) ends at (16, 156)
6. [B1] Curve concave down, 16 < t < 20 from (16, 156) to (20, 200)
7. [M1] Use relevant constant acceleration equations or the area property of a v-t graph
8. [A1] V = 10