Question

A force of $(3\hat{i}-1.5\hat{j})$ acts on 5 kg body. The body is at a position of $(2\hat{i}-3\hat{j})m$ and is travelling at $4m{s}^{-1}$.
The force acts on the body until it is at the position $(\hat{i}+5\hat{j})$ m. Assuming no other force does work on the body, the final speed of the body is

• A. $\sqrt{10}m/s$
• B. $5m/s$
• C. $\sqrt{5}m/s$
• D. $10m/s$
  

Answer 1

The correct option is A

$\sqrt{10}m/s$

Given, mass of the body = 5 kg

Force $\overrightarrow{F}=3\hat{i}-1.5\hat{j}$

$\therefore \overrightarrow{a}=\frac{3}{2}\hat{i}-\frac{3}{10}\hat{j}$

Now displacement , $\overrightarrow{s}=\left\{\right(\hat{i}+5\hat{j})-(2\hat{i}-3\hat{j}\left)\right\}m=(-\hat{i}+8\hat{j})m$

From work energy principle

$W=\overrightarrow{F}.\overrightarrow{S}=\frac{1}{2}m(v^2-u^2)$

$\Rightarrow v=\sqrt{10}m/s$