Question

A vehicle uses 250,000 J of energy to accelerate from rest. if the vehicle has a velocity of 50 m/s now, what is its mass? if the vehicle took 100 m to get up to full speed what force did it exert?

Answer 1

The mass can be found from conservation of energy: the work was spent to gain kinetic energy:

$$W=\frac12mv^2,\\\space\\ m=\frac{2W}{v^2}=200\text{ kg}.$$

The necessary acceleration to increase the speed from 0 to 50 m/s is

$$a=\frac{v^2}{2d}.$$

According to Newton's second law, the force is

$$F=ma=\frac{mv^2}{2d}=2500\text{ N}.$$