CIE AS & A Level Physics : 3.1 Momentum and Newton’s laws of motion – Exam style question – Paper 1

Question

A sprinter takes a time of 11.0 s to run a 100 m race. She first accelerates uniformly from rest, reaching a speed of \(10ms^{-1}\). She then runs at a constant speed of \(10ms^{-1}\) until the finish line. What is the uniform acceleration of the sprinter for the first part of the race?

A     \(0.5 m s^{–2}\)       B    \(0.91 m s^{–2}\)             C   \(1.7 m s^{–2}\)       D     \(5.0 m s^{–2}\)

Answer/Explanation

Ans:   D

Let the time of acceleration be t, then we have the total distance traveled in the acceleration phase and the constant velocity phase, given as,

100 = (1/2)at^2 + 10( 11-t)

Also we have,

v = at therefore, 

a = 10/t

substituting this in the above equation we get,

100 = (1/2)*( 10/t)*t^2 + 110 – 10t

100 = 5t – 10t + 110

t = 2 s

Hence the acceleration is therefore,

a = 10/2 = 5 m/s^2.

Hence the option D is correct.

Question

A single horizontal force F is applied to a block X which is in contact with a separate block Y, as shown.

The blocks remain in contact as they accelerate along a horizontal frictionless surface. Air resistance is negligible. X has a greater mass than Y.

Which statement is correct?

A    The acceleration of X is equal to force F divided by the mass of X.

B    The force that X exerts on Y is equal to F.

C    The force that X exerts on Y is less than F.

D    The force that X exerts on Y is less than the force that Y exerts on X.

Answer/Explanation

Ans:    C

The force that X exerts on Y is equal to the force that Y exerts on X which is equal to the mass of Y times the acceleration which is less than the force F which is the acceleration times the mass of X and Y. Hence the option (C) is correct.

Question

A car of mass 750 kg has a horizontal driving force of 2.0 kN acting on it. It has a forward horizontal acceleration of 2.0 m s^{–2}.

What is the resistive force acting horizontally?

A   0.50 kN             B   1.5 kN                  C    2.0 kN                 D   3.5 kN

Answer/Explanation

Ans:   A

The equation of motion of the car is given as,

F – F_r = ma

F_r = F – ma

= 2000 – 750*2

= 500 N = 0.5 kN

Hence the option (A) is correct.

Question

 A constant resultant force acts on an object in the direction of the object’s velocity. Which graph could show the variation with time t of the momentum p of the object?

       

Answer/Explanation

Ans:C

The force is given as the rate of change of momentum hence,

F = dp/dt

 

Question

A train, initially at rest at a station, has a uniform acceleration of 0.20 m s-2 until it reaches a speed of 20 m s -1. It travels for a time at this constant speed and then has a uniform deceleration of 0.40 m s -2 until it comes to rest at the next station. The distance between the two stations is 3000 m.
What is the time taken by the train to travel between the two stations?
75 s    150 s   C  230 s   D  300 s

Answer/Explanation

Ans: C

Let the time taken by the train be t s, then we have the time of acceleration is given as, 

t_a = v/a

= 20/0.2

 = 100 s

The time of deceleration is given as,

t_d = ( 20-0)/0.4 = 50 s.

Let t be the time of the motion with constant velocity then the distance traveled is given as,

D = (1/2)at_a + vt + vt_d- (1/2)a’ t_d^2

3000 = ( 1/2)*0.2*100^2+20t +20*50 -(1/2)*0.4*(50)^2

3000 = 1000 +20t +1000-500

t = 1500/20 = 75 s

Hence the total time is therefore,

T = t_a + t + t_d  = 100+75+50 = 225 s.

Hence the  closest option (C) is correct.

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