Question

For a body moving from position Xa to position Xb under a variable force, what is the work done?

(a) W = F * (X2 – X1)

(b) -W = F * (X2 – X1)

(c) W = -F * (X2 – X1)

(d) W = F * (X1 – X2)

This question was posed to me during an interview.

The origin of the question is Work-Energy Theorem for a Variable Force topic in division Work, Energy and Power of Physics – Class 11

Answer 1

The correct choice is (a) W = F * (X2 – X1)

The explanation is: Kinetic energy (K) = 1/2 x m x v^2

dK/dt = m*v*dv/dt

Force (F) = m*a

 = m*dv/dt

dK/dt = F*v

 = m*v*dv/dt

\(\int_{K1}^{K2}\) dK/dt = \(\int_{Xa}^{Xb}\) F * dX/dt

\(\int_{K1}^{K2}\) dK = \(\int_{Xa}^{Xb}\) F * dX

K2 – K1 = F (X2 – X1)

W = F * (X2 – X1).