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NEET 2007 (AIPMT) · Velocity, Acceleration & Variable Motion

Velocity, Acceleration & Variable Motion question from NEET 2007 (AIPMT)

Q41NEET 2007 · AIPMTMedium

Velocity, Acceleration & Variable Motion

A particle moving along x-axis has acceleration f, at time t, given by f = f0 $\left(1 - \frac{t}{T}\right),$ where f0 and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle's velocity (vx) is

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Answer: (c)

$f = 0$ when $t = T$
$v = \int_0^T f_0\left(1 - \dfrac{t}{T}\right)dt = f_0\left[t - \dfrac{t^2}{2T}\right]_0^T$
$v = f_0 T - \dfrac{f_0 T}{2} = \dfrac{1}{2}f_0 T$
So the answer is (c) $\dfrac{1}{2}f_0 T$ (positive).

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