Velocity and Acceleration1. A particle P travels in a straight line with constant acceleration 0.5ms-2. The initial speed of P

is 3ms-1. Finda) The speed of P after 4s,b) The time taken for P to travel a distance of 55m.

2.

The three (t,v) graphs in the diagram refer to three particles P, Q and R, each of which travels in a straight line for 20s. State which one of P, Q and R

a) Does not start from restb) Is not slowing down for 0<t<20.

The acceleration of P for 0<t<10 is 0.3ms-2.

c) Find the greatest speed of P.d) Find the distance travelled by Pe) Given that Q travels the same distance as P, find the greatest speed of Q.

3. A train travels along a straight track ABCD. It starts off from rest at A and comes too rest again at D. The distances AB and BC are 2880m and 3600m respectively. The train travels from B with a constant acceleration of 0.1ms-2, and continues onwards to C with constant speed. The train then decelerates uniformly from C to D. The total time for the journey from A to D is 750s.

a) Sketch the (t,v) graph for the journey. Calculate the values of t and v when the train is at B, and the value of t when the train is at C.

b) Find the distance AD.

4. A car starts from rest at the point A and moves in a straight line with constant acceleration for 20 seconds until it reaches the point B. The speed of the car at B is 30ms-1. Calculate

a) The acceleration of the carb) The speed of the car when it passes point C, where C is between point A and B and

AC= 40m

5. A motorist travelling at u ms-1 joins a straight motorway. On the motorway she travels with a constant acceleration of 0.07ms-2 until her speed has increased by 2.8ms-1.

a) Calculate the time taken for this increase in speedb) Given that the distance travelled while this increase takes place is 1050m, find u.

6. A cyclist, travelling with constant acceleration along a straight road, passes three points A, B and C, where AB= BC= 20m. The speed of the cyclist at A is 8ms-1 and at B is 12ms-1. Find the speed of the cyclist at C.

7.

The figure shows the (t,v) graph for the motion of a cyclist; the graph consists of three straight line segments. Use the information given on the graph to find the acceleration of the cyclist when t= 2 and the total distance travelled by the cyclist for 0<t<30.

Without any detailed calculations, sketch the displacement-time graph for this motion.

8. A car is waiting at traffic lights with a van behind it. There is a 1m gap between them. When the lights turn green the car accelerates at 1.5ms-2 until it reaches a speed of 15ms-1. It then proceeds at this speed. The van does the same, starting when the gap between the vehicles is 4m.

Find a formula for the distance travelled by the car in the first t seconds (0<t<10). Hence find the time interval between the car starting and the van starting.Using the same axis, draw velocity- time graphs for the car and the van. Hence find the gap between the vehicles when they are both going at 15ms-1.

9. Two runners, Alice and Belle, are leading the field in a long distance race. They are both running at 5ms-1, with Alice 10m behind Belle. When Belle is 50m from the tape, Alice accelerates but Belle doesn’t. What is the least acceleration Alice must produce to overtake Belle?

10. A woman stands on the bank of a frozen lake with a dog by her side. She skims a bone across the ice at a speed of 3ms-1. The bone slows down with deceleration of 0.4ms-2, and the dog chases it with acceleration of 0.6ms-2. How far out from the bank does the dog catch up with the bone?

11. A man is running for a bus at 3ms-1. When he is 100m from the bus stop, the bus passes him going at 8ms-1. If the deceleration of the bus is constant, at what constant rate should the man accelerate so as to arrive at the bus stop at the same instance as the bus?

12. a) A train travels from a station P to the next destination Q, arriving at Q exactly 5 minutes after leaving P. The (t, v) graph for the trains journey is approximated by three straight line segments, as shown in the figure.

i. Write down the acceleration of the train during the first minute of the journey.ii. Find the distance from P to Q.

b) On one occasion, when the track is being repaired, the train is restricted to a maximum speed of 10ms-1 for the 2000m length of track lying midway between P and Q. The train always accelerates and decelerates at the rate shown in the figure. When not accelerating or decelerating or moving at the restricted speed of 10ms-1, the train travels at 30ms-1. Sketch the (t, v) for the trains journey from P to Q when the restriction is in force, and hence find out how long the train takes to travel from P to Q on this occasion.

13.