KINEMATICS  -  v/t graphs

1.	The velocity-time graphs below show the motion of a car and a bicycle as they travel along a straight horizontal road. When t = 0, the car and bicycle pass a traffic light on the road. At the traffic light, the bicycle is travelling at a constant velocity of 5 m s–2, but the car is travelling at 3 m s–1 and accelerating.

(a)	(i)	Explain how the graph indicates that the acceleration of the car is constant.

(ii)	Find the acceleration of the car.

(b)	When t = T, the car has travelled twice as far from the traffic light as the bicycle. Find the value of T. 

2.	The velocity–time graph shows the motion of a particle P moving with constant acceleration.

	
	At times t = 2 and t = 5, P has velocities 3U and 5U respectively.

(a)	(i)	Find, in terms of U, the acceleration of P.

(ii)	Find, in terms of U, the distance travelled by P between the times t = 2 and t = 5.

(b)	When t = 5, the motion of P changes and subsequently P moves with a constant retardation. The particle P comes to rest after travelling a further 20 metres in the next 4 seconds.
	Find the value of U.

3.	A student attempts to model the motion of a bungee jumper. He draws the velocity–time graph shown below.

(a)	State the two non-zero times at which the velocity of the bungee jumper is zero.

(b)	Find the distance that the bungee jumper falls during the first 4 seconds.

(c)	Find the total distance travelled by the bungee jumper during the 5.6 seconds illustrated on the graph.

(d)	Find the acceleration of the bungee jumper during the first 2 seconds and hence state one problem with the proposed model.

(e)	Make one other criticism of the model, explaining its significance.

Solutions

1.	(a)		(i)  graph linear / straight line	
 	(ii) 	
	(b)  T = 21s	

2.       (a)	(i)	a = 		
	(ii)	s = 12U	
          (b)	U = 2	

3.        (a)	t = 4 and t = 5.6	
            (b)   	         50 m	
  (c)                       58 m	
           (d)	12.5 ms–2	
	Exceeds acceleration due to gravity therefore impossible.
	(e)	Acceleration will not be constant due to air resistance and elasticity.