Question

How large a force is required to accelerate a 1400-kg car from rest to a speed of 30 m/s in a distance of 80 m?

Answer 1

Let's first find the acceleration of the car:

$$v^2=v_0^2+2ad,$$ $$a=\dfrac{v^2-v_0^2}{2d},$$ $$a=\dfrac{(30\ \dfrac{m}{s})^2}{2\cdot80\ m}=5.62\ \dfrac{m}{s^2}.$$

Finally, we can find the force from the Newton's Second Law of Motion:

$$F=ma=1400\ kg\cdot5.62\ \dfrac{m}{s^2}=7868\ N.$$