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Question

A particle starts from rest with a time-varying acceleration a=(2t−4). Here t is in s and a in m/s2. The velocity-time graph of the particle will be a

A
parabola passing through origin.
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B
straight line not passing through origin.
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C
parabola not passing through origin
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D
straight line passing through origin
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Solution

The correct option is A parabola passing through origin.To find velocity, integrate acceleration w.r.t time, a=2t−4 ⇒dvdt=2t−4 ⇒∫v0dv=∫t0(2t−4)dt ⇒v=t2−4t Hence, v−t graph will be a parabola. Since initial velocity is zero, the parabola will pass through the origin.

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