Question

The relation between the time t and position x for a particle moving on x axis is given by t= px^2 + qx where p and q are constants . The relation between velocity v and acceleration a

Answer 1

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
hope it will help you