Question

A body is moving with velocity $30\text{m/s}$ towards east. After $10$ seconds its velocity becomes $40\text{m/s}$ towards north. The average acceleration of the body is

• A. $\sqrt{7}{\text{m/s}}^2$
• B. $7{\text{m/s}}^2$
• C. $1{\text{m/s}}^2$
• D. $5{\text{m/s}}^2$

Answer 1

The correct option is D $5{\text{m/s}}^2$

Average acceleration is given by
$<a>=\frac{\text{Change in velocity}}{\text{Total Time}}$
Here, final velocity is $40\hat{j}$ and initial velocity is $30\hat{i}$
So, change in velocity will be $\Delta \overrightarrow{v}=40\hat{j}-30\hat{i}$
or, $|\Delta \overrightarrow{v}|=\sqrt{{40}^2+(-30{)}^2}=50\text{m/s}$
Therefore, $<a>=\frac{|\Delta \overrightarrow{v}|}{t}=\frac{50}{10}=5{\text{m/sec}}^2$.