Question

A particle was at x=0 at t=0. It moves with velocity v along the positive x axis. If v changes with respect to x following the rule v=kx^0.5. How do its velocity and acceleration changes with time?

Answer 1

Answer:

v=k√x

v=dx/dt

x^(-0.5)DX=dt

integrate with limits 0 to x and 0 to t

2√x=kt

x=kt²/4

differentiate wrt fir velocity.

v= tk/2

differentiate again

a =k/2