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  4. The magnitude of velocity and acceleration and velocity of a particle moving in a plane, whose position vector r =3 t2 hat i +2 t 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.

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Q. The magnitude of velocity and acceleration and velocity of a particle moving in a plane, whose position vector $r =3 t^{2} \hat{ i }+2 t \hat{ j }+\hat{ k }$ 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.

TS EAMCET 2018

Solution:

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