Question

a body is acted upon by a force which is directly proportional to the distance covered ‘s' the work done will be proportional

Answer 1

F is directly proportional to the distance

⇒F=kx

⇒mv(dv/dt)=kx

⇒v(dv/dt)=kx/m

⇒∫v.dv/dt =k/m∫x.dx

⇒v²/2 =kx²/2m

⇒1/2mv²=kx²/2

⇒Δ1/2mv² ∝x²

⇒ W∝x²