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Question

# A particle located at x=0 at t=0, starts moving along the positives x−direction with a velocity ′v′ which varies as v=α√x, then velocity of particle varies with time as : (α is a constant)

A
vt
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B
vt2
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C
vt
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D
v= constant
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Solution

## The correct option is A v∝tThe velocity is given as, v=α√x dxdt=α√x dx√x=αdt ∫dx√x=∫αdt 2√x=αt+C Since, at t=0, x=0 so the value of C is 0. 2√x=αt x=14α2t2 The velocity is given as, v=dxdt =12α2t Thus, the velocity of particle is directly proportional to the time (v∝t).

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