Time to reach midpoint or specific position

6. A cyclist is moving along a straight horizontal road and passes a point \(A\). Five seconds later, at the instant when she is moving with speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), she passes the point \(B\). She moves with constant acceleration from \(A\) to \(B\). Given that \(A B = 40 \mathrm {~m}\), find

1. the acceleration of the cyclist as she moves from \(A\) to \(B\),
2. the time it takes her to travel from \(A\) to the midpoint of \(A B\).

6. A train travels for a total of 270 s along a straight horizontal track between two stations \(A\) and \(B\). The train starts from rest at \(A\) and moves with constant acceleration for 60 s until it reaches a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The train then travels at this constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) before it moves with constant deceleration for 30 s , coming to rest at \(B\).

1. Sketch below a speed-time graph for the journey of the train between the two stations \(A\) and \(B\). Given that the distance between the two stations is 4.5 km ,
2. find the value of \(V\),
3. find how long it takes the train to travel from station \(A\) to the point that is exactly halfway between the two stations. The train is travelling at speed \(\frac { 1 } { 4 } V \mathrm {~ms} ^ { - 1 }\) at times \(T _ { 1 }\) seconds and \(T _ { 2 }\) seconds after leaving station \(A\).
4. Find the value of \(T _ { 1 }\) and the value of \(T _ { 2 }\)

1. A van travels with constant acceleration along a straight horizontal road.

The van passes a point \(A\) with speed \(u \mathrm {~ms} ^ { - 1 }\) and 20 seconds later passes a point \(B\) with speed \(28 \mathrm {~ms} ^ { - 1 }\) The distance \(A B\) is 400 m .

1. Show that \(u = 12\)
2. Find the time taken for the van to travel from \(A\) to the midpoint of \(A B\). The van has mass 1200 kg .
   During its motion the van experiences a constant resistive force of magnitude 260 N
3. Find the magnitude of the driving force exerted by the engine of the van as it travels from \(A\) to \(B\).

4 Fig. 4 illustrates a straight horizontal road. A and B are points on the road which are 215 metres apart and M is the mid-point of AB . When a car passes A its speed is \(12 \mathrm {~ms} ^ { - 1 }\) in the direction AB . It then accelerates uniformly and when it reaches \(B\) its speed is \(31 \mathrm {~ms} ^ { - 1 }\). \begin{figure}[h] \end{figure}

1. Find the car's acceleration.
2. Find how long it takes the car to travel from A to B .
3. Find how long it takes the car to travel from A to M .
4. Explain briefly, in terms of the speed of the car, why the time taken to travel from A to M is more than half the time taken to travel from A to B .

3. A lorry accelerates uniformly from \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in 30 seconds.

1. Find how far it travels while accelerating.
2. Find, in seconds correct to 2 decimal places, the length of time it takes for the lorry to cover the first half of this distance.
   (6 marks)

1 Fig. 4 illustrates a straight horizontal road. \(A\) and \(B\) are points on the road which are 215 metres apart and \(M\) is the mid-point of AB . When a car passes A its speed is \(12 \mathrm {~ms} ^ { - 1 }\) in the direction AB . It then accelerates uniformly and when it reaches \(B\) its speed is \(31 \mathrm {~ms} ^ { - 1 }\). \begin{figure}[h] \end{figure}

1. Find the car's acceleration.
2. Find how long it takes the car to travel from A to B .
3. Find how long it takes the car to travel from A to M .
4. Explain briefly, in terms of the speed of the car, why the time taken to travel from A to M is more than half the time taken to travel from A to B .

A racing car moves with constant acceleration along a straight horizontal road. It passes the point \(O\) with speed 12 m s\(^{-1}\). It passes the point \(A\) 4 s later with speed 60 m s\(^{-1}\).

1. Show that the acceleration of the car is 12 m s\(^{-2}\). [2]
2. Find the distance \(OA\). [3]

The point \(B\) is the mid-point of \(OA\).

1. Find, to 3 significant figures, the speed of the car when it passes \(B\). [3]

A car moves in a straight line from \(P\) to \(Q\), a distance of \(420\) m, with constant acceleration. At \(P\) the speed of the car is \(8\) ms\(^{-1}\). At \(Q\) the speed of the car is \(20\) ms\(^{-1}\). Find

1. the time taken to travel from \(P\) to \(Q\), \hfill [2 marks]
2. the acceleration of the car, \hfill [2 marks]
3. the time taken for the car to travel \(240\) m from \(P\). \hfill [4 marks]

Given that the mass of the car is \(1200\) kg and the tractive force of the car is \(900\) N,

1. find the magnitude of the resistance to the car's motion. \hfill [3 marks]