How much energy is gained by a box of mass 20 kg when a man

(a) carrying the box waits for 5 minutes for a bus?

(b) runs carrying the box with a speed of 3 ms^-1 to catch the bus?

(c) raises the box by 0.5 m in order to place it inside the bus?

(g=10 ms^-2)

Given,

Mass = 20 kg

(a) As there is no displacement of the man, so work done is Zero.

(b) We know,

Work done = Kinetic energy of man = 1 / 2 × mass × (velocity)²

$\text{Work done} = \text{Kinetic energy of man} \\[0.5em] = \dfrac{1}{2} \times \text{mass} \times \text{velocity}^2 \\[0.5em] = \dfrac{1}{2} \times 20 \times 3^2 \\[0.5em] = \dfrac{1}{2} \times 20 \times 9 \\[0.5em] = 90 J \\[0.5em]$

∴ Energy Gained = 90 J

(c) We know,

Potential energy = mgh

$\text{PE} = 20 \times 10 \times 0.5 \\[0.5em] \Rightarrow U = 100 J \\[0.5em]$