Question

A particle has an initial velocity $v=3\hat{i}+4\hat{j}m/s$ and acceleration of $0.4\hat{i}+0.3\hat{j}m/s^2$. Its speed after $10s$ is

• A. $10m/s$
• B. $7m/s$
• C. $7\sqrt{2}m/s$
• D. $8.5m/s$

Answer 1

The correct option is C $7\sqrt{2}m/s$

Applying $1^{st}$ law of motion in both $x$ and $y$ direction respectively,
In $x$-direction;
$V_x=u_x+a_{x}t=3+0.4\times 10=7m/s$
In $y$-direction;
$V_y=u_y+a_{y}t=4+0.3\times 10=7m/s$
Total speed=
$v=\sqrt{v_x^2+v_y^2}=7\sqrt{2}m/s$