Question

The motor of an electric vehicle runs at an average of 50 hp for one hour and 25 minutes. Determine the total energy. Write the result in engineering notation and with SI units.

Answer 1

Answer:

The total energy of the motor of the electric vehicle is 1.902 × 10⁸ joules.

Explanation:

Power is the rate of change of work in time, since given input is average power, the total energy ($\Delta E$) of the motor of the electric vehicle, measured in joules, is determined by this formula:

$\Delta E = \dot W \cdot \Delta t$

Where:

$\dot W$ - Average power, measured in watts.

$\Delta t$ - Time, measured in seconds.

Now, let convert average power and time into watts and seconds, respectively:

Average Power

$\dot W = (50\,hp)\times \frac{746\,W}{1\,hp}$

$\dot W = 3.730\times 10^{4}\,W$

Time

$\Delta t = (1\,h)\times \frac{3600\,s}{1\,h} + (25\,min)\times \frac{60\,s}{1\,min}$

$\Delta t = 5.100\times 10^{3}\,s$

Then, the total energy is:

$\Delta E = (3.730\times 10^{4}\,W)\cdot (5.100\times 10^{3}\,s)$

$\Delta E = 1.902\times 10^{8}\,J$

The total energy of the motor of the electric vehicle is 1.902 × 10⁸ joules.