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Question

A particle located at x=0 at t=0, starts moving along the positives xdirection with a velocity v which varies as v=αx, 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 vt

The velocity is given as,

v=αx

dxdt=αx

dxx=αdt

dxx=αdt

2x=αt+C

Since, at t=0, x=0 so the value of C is 0.

2x=αt

x=14α2t2

The velocity is given as,

v=dxdt

=12α2t

Thus, the velocity of particle is directly proportional to the time (vt).


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