Q.

A body starts from rest with uniform acceleration a. The acceleration of the body as function of time t is given by the equation a = pt, where p is a constant, then the displacement of the particle in the time interval t = 0 to t = t1 will be

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a

12pt13

b

13pt12

c

12pt12

d

16pt13

answer is D.

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Detailed Solution

Integrate twice to convert a-t equation into s-t equation.∵                    ⇒         ∫0vdv=∫0ta·dt⇒v=∫0tpt·dt=pt22∵            ⇒          ∫0s ds=∫0t1vdt⇒s=16pt13
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A body starts from rest with uniform acceleration a. The acceleration of the body as function of time t is given by the equation a = pt, where p is a constant, then the displacement of the particle in the time interval t = 0 to t = t1 will be