Question

How much work must be done to accelerate an 800kg car from 15m/s to 30m/s?

Answer 1

The energy-work theorem gives

$$\Delta E=W\\ \frac{mv_2^2}{2}-\frac{mv_1^2}{2}=W$$ $$W=\rm\frac{800\:kg*(30\:m/s)^2}{2}-\rm\frac{800\:kg*(15\:m/s)^2}{2}$$

$$W=\rm 270\: 000\; J$$