1.State and prove the Work-Energy Theorem for a constant force.
Sol: $W = F s = (m a) s = m \left(\frac{v^2 - u^2}{2s}\right) s = \frac{1}{2} m v^2 - \frac{1}{2} m u^2 = \Delta K$.
2.A force $\vec{F} = (3\hat{i} + 4\hat{j})\text{ N}$ displaces a body by $\vec{d} = (5\hat{i} + 2\hat{j})\text{ m}$. Find work done.
Sol: $W = \vec{F} \cdot \vec{d} = 3(5) + 4(2) = 15 + 8 = 23\text{ Joules}$.
3.A ball of mass $0.2\text{ kg}$ is dropped from height $10\text{ m}$. Find its kinetic energy just before hitting the ground.
Sol: By conservation of mechanical energy: $K = m g h = 0.2(9.8)(10) = 19.6\text{ Joules}$.
4.Define average power and instantaneous power with SI units.
Sol: Average power $P_{avg} = \frac{\Delta W}{\Delta t}$, Instantaneous power $P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}$. SI unit: Watt ($\text{W} = \text{J/s}$).
