4. A motor scooter and a van set off along a straight road. They both start from rest at the same time and level with each other. The scooter accelerates with constant acceleration until it reaches its top speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It then maintains a constant speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The van accelerates with constant acceleration for 10 s until it reaches its top speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 } , V > 20\). It then maintains a constant speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The van draws level with the scooter when the scooter has been travelling for 40 s at its top speed. The total distance travelled by each vehicle is then 850 m .

1. Sketch on the same diagram the speed-time graphs of both vehicles to illustrate their motion from the time when they start to the time when the van overtakes the scooter.
2. Find the time for which the scooter is accelerating.
3. Find the top speed of the van.