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Question

The velocity of a particle moving in the positive direction of x axis varies as v=10x (v is in ms1,x is in m). Assuming that at t=0, particle was at x=0. Then,

A
The initial velocity of the particle is zero
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B
The initial velocity of the particle is 2.5 ms1
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C
The acceleration of the particle is 2.5 ms2
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D
The acceleration of the particle is 50 ms2
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Solution

The correct option is D The acceleration of the particle is 50 ms2
Given v=10x.......(1)
dxdt=10xdxx=10dt
2x=10t+c
Given that at t=0,x=0,
c=0
2x=10tx=25t2
Substituting in (1),
v=50t
At t=0,v=0
Differentiating v
a=dvdt=50 ms2

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