Question

A body is moving with velocity $30m{s}^{-1}$ towards east. After $10s$ its velocity becomes $40m{s}^{-1}$ towards north. the average acceleration of the body is

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

Answer 1

The correct option is C $5m{s}^{-2}$

Given,

$\overrightarrow{u}=30\hat{i}m/s$

$\overrightarrow{v}=40\hat{j}m/s$

$\Delta t=10s$

Change in velocity, $\Delta \overrightarrow{v}=\overrightarrow{v}-\overrightarrow{u}$

$\Delta \overrightarrow{v}=40\hat{j}-30\hat{i}$

$|\Delta \overrightarrow{v}|=\sqrt{(40{)}^2+(-30{)}^2}=50m/s$

The average acceleration of the body is

$a_{avg}=\frac{|\Delta \overrightarrow{v}|}{\Delta t}$

$a_{avg}=\frac{50}{10}$

$a_{avg}=5m/s^2$

The correct option is C.