Question

The relation between time and displacement of a moving object is given as t= ax² + bx, where a, b are constants. Prove that the acceleration of the body is( -2av³)

Answer 1

similar question the relation between time t and positon x for a particle moving on x axis is given by t =p(x)square +qx find relation between velocity and acceleration?

note: dx/dt = v dv/dx=a and (dv/dx)*(dx/dt)=a

t=px²+qx

on differentiating wrt t , we have

1=2pxv+qv .....(1)

on differentiating wrt x , we have

0=2pv+2px.dv/dx +q.dv/dx

0=2pv+2px.(a/v) +q.(a/v)

0=2pv²+2pxa +qa ....(2)

from (1) and (2) ..we have

2pv³+a=0
a= -2pv³