A body starting from rest moves with constant acceleration 'a'. This acceleration is a pr where p is a constant. What is the displacement of particle in a time interval=0 to t = `t_1` ?

Options

A. `(1)/(3)pt_(1)^(3)`
B. `(1)/(4)pt_(1)^(2)`
C. `(-1)/(6)pt_(1)^(3)`
D. `(1)/(4)pt_(1)^(3)`

Answer

c

Explanation

Here a=pt
dv=pt dt
`:. v=int_(0)^(h) pt dt=1/2pt_(1)^(2)`
But v=dx/dt
`:. Dx=int_(0)^(t_1) 1/2pt_(1)^(2) dt`
`=1/2p(t_(1)^(3))/(3)`
`=(1)/(6)pt_(1)^(3)`