Question

The force acting on a body of mass 10kg is (2i+j-k)N. If the body is initially at rest, determine the magnitude of velocity at the end of 20s

Answer 1

Let the force be $\mathbf{F} = 2\mathbf{i} + \mathbf{j}-\mathbf{k}$. Then, according to the Newton's law, the acceleration of the body is:

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

where $m = 10kg$ is the mass of the body.

From the kinematic equation the velocity is expressed as follows (if body was initially at rest):

$$\mathbf{v} = \mathbf{a}t$$

where $t = 20s$ is the time. Thus, obtain:

$$\mathbf{v} = \dfrac{t}{m}\mathbf{F} = \dfrac{20s}{10kg}\cdot(2\mathbf{i} + \mathbf{j}-\mathbf{k})N = \\ =(4\mathbf{i} + 2\mathbf{j}-2\mathbf{k})m/s$$

The magnitude is then:

$$v = \sqrt{4^2 + 2^2 + (-2)^2} \approx 4.9m/s$$

Answer. 4.9 m/s.