A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after $10s$ is

The correct option is C

$7\sqrt{2}units$

Step 1: Given data

Initial velocity, $u=3\hat{i}+4\hat{j}$

Acceleration, $a=0.4\hat{i}+0.3\hat{j}$

Time, $t=10s$

Step 2: Find Final velocity

Final velocity (v) is given by

using the first equation of motion,

$$\begin{gathered} v=u+at \\ v=3\hat{i}+4\hat{j}+(0.4\hat{i}+0.3\hat{j})10 \\ v=7\hat{i}+7\hat{j} \end{gathered}$$

$$\begin{gathered} V=\sqrt{7^2+7^2} \\ V=7\surd 2units \end{gathered}$$

Hence, option C is correct.