Question

A body is moving with velocity $30m{s}^{-1}$ towards east. After $10s$ its velocity becomes $40m{s}^{-1}$ towards the north. The average acceleration of the body is $m{s}^{-2}$.

• A. $5$
• B. $1$
• C. $7$
• D. $\sqrt{7}$

Answer 1

The correct option is A

$5$

Step 1.Given data:

Initial velocity $V_i=30\overrightarrow{i}m/s$

Final velocity, $V_f=40\overrightarrow{j}m/s$

Step 2. Finding the average acceleration.

By using the formula of the acceleration vector

Acceleration vector $\overrightarrow{a}=\frac{v_f-v_i}{∆t}$

$\overrightarrow{a}=\frac{(40\overrightarrow{j}-30\overrightarrow{i})}{10}m{s}^{-2}$

$=(4\overrightarrow{j}-3\overrightarrow{i})m{s}^{-2}$

Average acceleration, $\left|\overrightarrow{a}\right|$ $=\sqrt{\left(4^2+3^2\right)}$

$a=5m{s}^{-2}$

Therefore, the average acceleration is $5m{s}^{-1}$.

Hence, correct option is $\left(A\right)$.