A lorry is moving along a straight horizontal road with constant acceleration. The lorry passes a point \(A\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 } , ( u < 34 )\), and 10 seconds later passes a point \(B\) with speed \(34 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Given that \(A B = 240 \mathrm {~m}\), find
the value of \(u\),
the time taken for the lorry to move from \(A\) to the mid-point of \(A B\).
A car is travelling along a straight horizontal road. The car takes 120 s to travel between two sets of traffic lights which are 2145 m apart. The car starts from rest at the first set of traffic lights and moves with constant acceleration for 30 s until its speed is \(22 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car maintains this speed for \(T\) seconds. The car then moves with constant deceleration, coming to rest at the second set of traffic lights.
Sketch, in the space below, a speed-time graph for the motion of the car between the two sets of traffic lights.
Find the value of \(T\).
A motorcycle leaves the first set of traffic lights 10 s after the car has left the first set of traffic lights. The motorcycle moves from rest with constant acceleration, a \(\mathrm { m } \mathrm { s } ^ { - 2 }\), and passes the car at the point \(A\) which is 990 m from the first set of traffic lights. When the motorcycle passes the car, the car is moving with speed \(22 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find the time it takes for the motorcycle to move from the first set of traffic lights to the point \(A\).