A 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=t_(1)` will be

Options

A. `(1)/(2)pt_(1)^(3)`
B. `(1)/(3)pt_(1)^(2)`
C. `(1)/(2)pt_(1)^(2)`
D. `(1)/(2)pt_(1)^(3)`

Answer

D

Explanation

Integrate twice to convert a-t equation into s-t equation.
`because a=(upsilon)/(t) rArr upsilon = at`
`rArr int d upsilon int a. dt rarr upsilon int pt. dt = (pt^(2))/(2)`
`because s=upsilonxxt rArr ds = upsilon dt`
`rArr int ds = int upsilon dt rArr s=(1)/(6)pt^(3)`