Question

A particle has initial velocity $(2\overrightarrow{i}+3\overrightarrow{j})$ and acceleration $(0.3\overrightarrow{i}+0.2\overrightarrow{j})$. The magnitude of velocity after 10 seconds will be

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

Answer 1

The correct option is D 5$\sqrt{2}$ units

Velocity after time ${}^{\prime }{t}^{\prime }=(u_x+a_{x}t)\overrightarrow{i}+(u_y+a_{y}t)\overrightarrow{j}$

$\Rightarrow \overrightarrow{a}=[2+0.3(10\left)\right]\overrightarrow{i}+[3+0.2(10\left)\right]\overrightarrow{j}=5\overrightarrow{i}+5\overrightarrow{j}$

So, The magnitude of velocity after 10 seconds will be

$|\overrightarrow{a}|=\sqrt{5^2+5^2}=5\sqrt{2}$ units.

Therefore, D is correct option.