Question

A particle is moving eastward with a velocity $5{ms}^{-1}$. In $10s$ the velocity changes to $5{ms}^{-1}$ northwards. The average acceleration in this time is:

• A. $\frac{1}{\sqrt{2}}{ms}^{-2}$ towards North - West
• B. $\frac{1}{2}{ms}^{-2}$ towards North - West
• C. $\frac{1}{\sqrt{2}}{ms}^{-2}$ towards North - East
• D. $\frac{1}{2}{ms}^{-2}$ towards North - East

Answer 1

Answer: (A)

$\frac{1}{\sqrt{2}}{ms}^{-2}$ towards North - West

Given: Initital velocity, $v_i=5\hat{i}$

Final velocity, $v_f=5\hat{j}$

Time, $t=10sec$

Average acceleration, $\overrightarrow{a}=\frac{\overrightarrow{v_f}-\overrightarrow{v_i}}{t}=\frac{5\hat{j}-5\hat{i}}{10}=0.5\hat{j}-0.5\hat{i}$

$\left|\overrightarrow{a}\right|=\sqrt{{0.5}^2+{0.5}^2}=\sqrt{2}\times 0.5=\frac{1}{\sqrt{2}}{ms}^{-2}$ and directed North-West