A particle moving along a straight path has an acceleration

A particle moving along a straight path has an acceleration defined by a = 5.0s^0.5 m/s^2, where s is in meters. If the particle starts from rest at s = 0, find its speed when s = 40 meters.

Solution

>> As, acceleration, a = v*(dv/ds)

>> 5*s^0.5 = v*dv/ds

=> 5*s^0.5 *ds = vdv

Integrating both sides,

=> (5/1.5)*s = v²/2 + C

>> Given, v = 0 at s = 0

=> C = 0

=> v = 2.58*s^0.5

>> So, When s = 40 m,

=> v = 2.58*40^0.5

=> Velocity at required point = 16.32 m/s