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