Discussion
The speed of an object of mass 20 kg increases from 2 m/s to 6 m/s in 10 s.
The power required, in Watts, is:
Answer: C
The power required is 32 W.
The work done equals the gain in kinetic energy, and the average power is that work divided by the time taken:
\[ \begin{aligned} \Delta K &= \tfrac{1}{2} \times 20 \times (6^{2} - 2^{2}) \\ &= 10 \times 32 = 320\ \text{J} \\ P &= \frac{320}{10} = 32\ \text{W} \end{aligned} \]
Forgetting the half in \(\frac{1}{2}mv^2\) gives 64 W. The work depends on the change in \(v^2\), 36 − 4, not on the change in \(v\), and 54 W and 72 W do not follow from it.
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