M1 June 2011 Q4
4. A girl runs a 400 m race in a time of 84 s. In a model of this race, it is assumed that, starting from rest, she moves with constant acceleration for 4 s, reaching a speed of 5 m s\(^{-1}\). She maintains this speed for 60 s and then moves with constant deceleration for 20 s, crossing the finishing line with a speed of \(V\) m s\(^{-1}\).
(a) Sketch, in the space below, a speed-time graph for the motion of the girl during the whole race. (2)
(b) Find the distance run by the girl in the first 64 s of the race. (3)
(c) Find the value of \(V\). (5)
(d) Find the deceleration of the girl in the final 20 s of her race. (2)
| Scheme | Marks |
|---|---|
| Shape | B1 |
| Figs | B1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(\left(\tfrac{1}{2} \times 4 \times 5\right) + 60 \times 5\) | M1 A1 |
| \(= 310\) | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| \(\dfrac{(5 + V)}{2} \times 20 = (400 - 310)\) | M1 A2 ft |
| \(V = 4\) | DM1 A1 |
| (5) |
| Scheme | Marks |
|---|---|
| \(\dfrac{5 - 4}{20} = 0.05\) ms\(^{-2}\) | M1 A1 |
| (2) | |
| (12 marks) |