Question

Particle has an initial velocity $(6\hat{i}+8\hat{j})m{s}^{-1}$ and $(0.8\hat{i}+0.6\hat{j})m{s}^{-2}$ an acceleration. Its speed after 10 s is:

• A. $20m{s}^{-1}$
• B. $7\sqrt{2}m{s}^{-1}$
• C. $10m{s}^{-1}$
• D. $14\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is D $14\sqrt{2}m{s}^{-1}$

We know,

$v=u+at$

Here,

$u=(6\hat{i}+8\hat{j})m/s$

$a=(0.8\hat{i}+0.6\hat{j})m/s^2$

$t=10sec$

Substituting values

$v=(6\hat{i}+8\hat{j})+(0.8\hat{i}+0.6\hat{j})\times 10$

$v=6\hat{i}+8\hat{j}+8\hat{i}+6\hat{j}$

$v=14\hat{i}+14\hat{j}$

Magnitude of speed will be,

$|v|=\sqrt{{14}^2+{14}^2}$

$|v|=14\sqrt{2}m/s$