Question

The magnitude of velocity and acceleration and velocity of a particle moving in a plane, whose position vector $r=3t^2\hat{i}+2t\hat{j}+\hat{k}$ at $t=2$ s are respectively
In the question paper sequence is given, (acceleration and velocity) which is not matching with any of option given.

• A. $\sqrt{148},6$
• B. $\sqrt{144},6$
• C. $\sqrt{13},3$
• D. $\sqrt{14},3$

Answer 1

Answer: (A)

Given, $r=3t^2\hat{i}+2\hat{j}\mathbf{j}+\hat{k}$
(i) Velocity vector, $v=\frac{dr}{dt}=6\hat{i}+2\hat{j}$
Magnitude of velocity vector,
$|v{|}_{t=2}=\sqrt{(12{)}^2+(2{)}^2}=\sqrt{148}$
(ii) Acceleration vector, $a=\frac{dv}{dt}=6\hat{i}$
Magnitude of acceleration $|a{|}_{t=2}=\sqrt{\left(6^2\right)}=6$