# A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v = x a . The displacement of the particle varies with time as ?

Jitender Singh IIT Delhi
7 years ago
Ans:
$v = ax$
$\frac{dx}{dt} = ax$
$\frac{dx}{x} = adt$
$\int \frac{dx}{x} = a\int dt$
$lnx = at + c$
$\Rightarrow x = e^{at+c}$
Thanks & Regards
Jitender Singh
IIT Delhi