Question

A particle has initial velocity $(2\hat{i}+3\hat{j})$ and acceleration $(0.3\hat{i}+0.2\hat{j})$ the magnitude of the velocity after $10s$ will be:

• A. $9\sqrt{2}units$
• B. $5\sqrt{2}units$
• C. $9units$
• D. $5units$

Answer 1

The correct option is B

$5\sqrt{2}units$

Step 1: Given data

Initial velocity,$u=(2\hat{i}+3\hat{j})$

Acceleration, $a=(0.3\hat{i}+0.2\hat{j})$

Time, $t=10s$

Step 2: To find

The velocity of the particle after $10s$.

Step 3: Formula used

$v=u+at$

where $v$ is final velocity, $u$ is initial velocity, $a$ is acceleration and $t$ is the time taken.

Step 4: Calculation

$v=u+at$

Substituting the values in the equation,

$$\begin{gathered} v=(2\hat{i}+3\hat{j})+(0.3\hat{i}+0.2\hat{j})\times \left(10\right) \\ \Rightarrow v=2\hat{i}+3\hat{j}+3\hat{i}+2\hat{j} \\ \Rightarrow v=5\hat{i}+5\hat{j} \end{gathered}$$

Taking the magnitude of $v$,

$$\begin{gathered} \left|v\right|=\sqrt{5^2+5^2} \\ \Rightarrow \left|v\right|=\sqrt{2\times 5^2} \\ \Rightarrow \left|v\right|=5\sqrt{2}units \end{gathered}$$

Therefore the magnitude of velocity of the particle after $10s$ is $5\sqrt{2}units$.