Question

Derive a relation between kinetic energy and momentum. [3 Marks]

Answer 1

Let the mass of the object be m and the speed of the object be v.

1. Kinetic energy (KE) = $\frac{1}{2}m{v}^2$ ................... (i) [1 Mark]

2. Momentum (P) = mv ...................(ii) [1 Mark]

Dividing and multiplying equation (i) by m, we get,

KE = $\frac{{\left(mv\right)}^2}{2m}$ .....................(iii)

3. Now, substituting the value of P from eq (ii) in eq (iii), we get,

KE = $\frac{P^2}{2m}$ [1 Mark]