The velocity of a particle moving in the positive direction of x− axis varies as v=10√x (v is in ms−1,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 2.5ms−1
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C
The acceleration of the particle is 2.5ms−2
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D
The acceleration of the particle is 50ms−2
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Solution
The correct option is D The acceleration of the particle is 50ms−2 Given v=10√x.......(1) dxdt=10√x⇒∫dx√x=10∫dt ⇒2√x=10t+c
Given that at t=0,x=0, ∴c=0 ∴2√x=10t⇒x=25t2
Substituting in (1), v=50t ∴Att=0,v=0
Differentiating v a=dvdt=50 ms−2