Question

12 A force of 2i+7j N acts on a body of mass 5kg for 10 seconds. The body was initially moving with constant velocity of i−2j m/s. Find the final velocity of the body in m/s, in vector form

Answer 1

A force of $2\tilde{\iota} + 7\tilde{\jmath}$ Nacts on a body of mass $5\mathrm{kg}$ for 10 seconds. The body was initially moving with constant velocity of $\tilde{\iota} - 2\tilde{\jmath}\frac{m}{s}$. Find the final velocity of the body in $\frac{m}{s}$, in vector form.

Solution.

According to Newton's second law:

$$\vec{a} = \frac{\vec{F}}{m} = \frac{2\tilde{\iota} + 7\tilde{\jmath}}{5} = 0,4\tilde{\iota} + 1,4\tilde{\jmath} \frac{m}{s^2},$$

where $\vec{F}$ is the force acting on the body, $m$ is the mass of the body and $\vec{a}$ is the acceleration of the body.

We have the uniformly accelerated motion because the acceleration $\vec{a}$ don't depend on time. Then the velocity of the body is:

$$\vec{v} = \overrightarrow{v_0} + \vec{a}t = \tilde{\iota} - 2\tilde{\jmath} + (0,4\tilde{\iota} + 1,4\tilde{\jmath}) \cdot 10 = 5\tilde{\iota} + 12\tilde{\jmath} \frac{m}{s},$$

where $\overrightarrow{v_0}$ is the initial velocity and $t$ is the time of the acting of the force.

**Answer**: $5\tilde{\iota} + 12\tilde{\jmath} \frac{m}{s}$.