Answer
In d), it is not possible for mechanical energy to be conserved.
Work Step by Step
According to the principle of conservation of mechanical energy, $$E_f-E_0=0$$ $$\Big(\frac{1}{2}mv_f^2+mgh_f\Big)-\Big(\frac{1}{2}mv_0^2+mgh_0\Big)=0$$ $$\frac{1}{2}m(v_f^2-v_0^2)=mg(h_0-h_f)$$
This equation means:
- If a car moves up a hill, or $(h_0-h_f)\lt0$, it follows that $(v_f^2-v_0^2)\lt0$, or the car's velocity has to continually decrease.
- If a car moves down a hill, or $(h_0-h_f)\gt0$, it follows that $(v_f^2-v_0^2)\gt0$, or the car's velocity has to continually increase.
- If a car moves along level ground, or $(h_0-h_f)=0$, it follows that $(v_f^2-v_0^2)=0$, or the car's velocity is constant.
Therefore, only in d) is it not possible for mechanical energy to be conserved.
