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Question

Figure depicts the motion of a particle moving along an x axis with a constant acceleration. The figure's vertical scaling is set by xs = 6.0 m. What is the particle's acceleration?


A

- 4 m/

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B

+4 m/

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C

+ 1 m/

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D

+ 2 m/

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Solution

The correct option is B

+4 m/


The given graph is a position time graph. This means that at t = 0 the particle is at x = -2

Don't assume the displacement = -2m

That would be wrong.

Since the particle is moving with constant acceleration. That means we can use the equations of motion

Now which one to use

s = ut + 12at2 we have s— t relation.

Now at t =1 particle has reached x = 0

So the displacement will be 2 m

From x= — 2 to x = 0. Displacement = final position— starting position.

2 = u(1) + 12a(1)2

2u + a = 4.............(1)
At t = 2 particle has reached x = 6. So after 2 secfrom start the particle is 8 cm for from starting point.

8=u(2)+12a(2)2

2u + 2a = 8

u + a = 4 .... (2)

from equation (1) and (2) we get u + 4 = 4

u = 0 . ... (3)

Substituting (3) in (2) get a = +4 m/s2

Acceleration =4 m/s2


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