Question

How fast is a 10 kg box going to be moving from rest after 3 seconds if a 200 N force is applied to the left and a 50 N force is applied to the right?

Answer 1

The resultant force applied to the box is:

$$F = 200N-50N = 150N$$

The '-' sign is because the forces directed to the left and to the right are opposite. The resultant force is directed to the left, since $200N>50N$.

According to the second Newton's law, the acceleration of the box is:

$$a = \dfrac{F}{m}$$

where $m = 10kg$ is the mass of the box. According to the kinematic equation, the velocity of the box is given as follows:

$$v = v_0 +at$$

where $v_0 = 0$ is the initial velocity of the box (equal to 0 since it starts from rest), and $t = 3s$ is the time. Thus, obtain:

$$v = \dfrac{F}{m}t\\ v = \dfrac{150N}{10kg}\cdot 3s = 45m/s$$

Answer. 45 m/s.