(Solved): make ID a random variable  Determine the power required for the car to climb a \( (100+1 D) \) ...

Determine the power required for the car to climb a \( (100+1 D) \) meter long uphill road with a \( (30+I D) \) degree slope as shown in (30-ID) seconds at... a) A constant velocity b) From rest to a final velocity of \( 30 \mathrm{~m} / \mathrm{s} \) c) From \( 35 \mathrm{~m} / \mathrm{s} \) to a final velocity of \( 5 \mathrm{~m} / \mathrm{s} \) Disregard friction, air drag, and rolling resistance. Indicate power put into the system as positive and power taken out of the system as negative. \[ \begin{array}{l} \left.\left.\dot{W}=\dot{W}_{p}=m g \Delta Z / \Delta t ; b\right) W=\dot{W}_{a}+\dot{W}_{p}=\left(\frac{1}{2} m\left(V_{2}^{2}-V_{1}^{2}\right)+m g \Delta Z\right) / \Delta t ; \text { and c) }\right) W^{W}=W_{a}+W_{p}= \\ \left.\left(\frac{1}{2} m\left(V_{2}^{2}-V_{1}^{2}\right)+m g \Delta Z\right) / \Delta t\right) \end{array} \]