Question

The position-time graph of a particle of mass 2 kg moving along x-axis is as shown in the figure. The magnitude of impulse on the particle at t = 2 s is

(1) 40Ns
(2) 20 Ns
(3) 10 Ns
(4) zero
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Answer 1

Answer:

(1) 40Ns

Explanation:

We need to check Momentum before and after the 2s mark,

From 0s to 2s, V = -20/2 = -10m/s ... Initial

From 2s to 4s, V = 20/2 = 10m/s .... Final

Given mass = 2kg

Therefore change in momentum,

(P)f - (P)i = (10×2) - ( -10×2)

= 20 - (-20)

= 20 + 20 = 40 Ns

Answer 2

The position-time graph of a particle of mass 2 kg moving along x - axis is as shown in the figure.

We have to find the magnitude of impulse on the particle at t = 2 sec.

Impulse : It is the change of linear momentum of a particle. unit of impulse is the same as that of linear momentum.

It is also defined as product of the force acting on the particle and time duration.

graph of motion of particle between 0 and 2 sec is a straight line, so the velocity during this time must be constant and that is the slope of graph.

velocity of particle between 0 and 2 sec = slope of graph between 0 and 2s

= (0 - 20)m/(2 - 0)s

= -10 m/s

now velocity of particle between 2sec to 4s = slope of graph between 2s and 4s

= (20 - 0)m/(4 - 2)s

= 10m/s

you see, the velocity of the particle changes -10 m/s to 10 m/s.

so the impulse of the particle at 2s = change in linear momentum of the particle at 2s

= 2 kg × 10 m/s - 2 kg × -10 m/s

= 40 kgm/s

= 40 Ns

Therefore the correct option is (1) 40 Ns.