The velocity of a particle moving in positive direction of x-axis is given as v^2=x.if the particle was located at origin initially,find the position as function of time.?

Answer 1

A little calculus is needed for this problem.

v = x^1/2 = dx/dt

The differential equation: x^1/2 = dx/dt can be solved by the method of separation of variables.

dt = dx/ x^1/2 Integrate both sides

t + c = 2 x^1/2 so x(t) = [( t + c) / 2 ]² c is a constant of integration

Since x(0) = 0 this implies that c = 0

Finally x(t) = ( t/2)²