Question

The slope of kinetic energy (on y-axis) and linear displacement (on x-axis) graph of a body gives the rate of change of:

• A. Linear momentum
• B. Linear velocity
• C. Force
• D. Angular momentum

Hint:

The slope of kinetic energy vs. displacement is the rate of work done per unit distance, which is force.

Answer 1

The Correct Option is C

Kinetic energy is $ {KE} = \frac{1}{2} m v^2 $. The slope of the graph is: \[ \frac{d({KE})}{ds} = \frac{d}{ds} \left( \frac{1}{2} m v^2 \right) = m v \frac{dv}{ds} \] Since $ \frac{dv}{ds} = \frac{dv}{dt} \cdot \frac{dt}{ds} = \frac{a}{v} $, where $ a $ is acceleration: \[ \frac{d({KE})}{ds} = m v \cdot \frac{a}{v} = m a \] Since $ m a = F $ (force), the slope represents force, matching option (3).