Question

A particle of mass m moves on a straight line with its velocity varying with the distance travelled according to the equation v = a√x, where a is a constant. Find the total work done by all the forces during a displacement from x = 0 to x = d.

Answer 1

Answer:

Answer: W=1/2ma2d

Work done due to a constant force W=Fd.

Constant Force = mass × acceleration.

Acceleration is given by

dvdt=dv/dx*dxdt

⇒=dv/dt=a2x−−√ax−−√=1/2a2

⇒W=1/2ma2d

Answer 2

Answer:

W=1/2ma2d

Work done due to a constant force W=Fd.

Constant Force = mass × acceleration.

Acceleration is given by

dvdt=dv/dx*dxdt

⇒=dv/dt=a2x−−√ax−−√=1/2a2

⇒W=1/2ma2d