Question

if a=-k√v and given when t=0,v=u. then find x and t?​

Answer 1

Answer: a= dv/ dt = -k√v

dv/√v = -k*dt

Integrating on both sides. When t=0, velocity is u and let when t= t, velocity is v

So, 2* √v - 2*√u = -kt

√v = √u -kt/2

Squaring on both sides

v = u +k^2 *t^2 /4 - √u *kt

dx/dt = u +k^2 *t^2 /4 - √u *kt

dx = (u +k^2 *t^2 /4 - √u *kt)dt

Integrating from 0 to x when t varies from 0 to t

x = ut+ (k^2 *t^3)/12 - (√u *k*t^2)/2

Explanation: