An object of mass 3 ~kg is at rest. Now a force F=6 t^2 i +4 j is applied on the object then the velocity of the object at t=3 ~s is:

Correct answer: B. 18 i +6 j From question a = F m =2 t^2 i +(4)/(3) t j d V =(2 t^2 i +(4)/(3) t j ) d t Integrated both sides, We have, V =2[(t^3)/(3)] i +(4)/(3)[(t^2)/(2)] j at t=3 sec, V =(2)/(3)(3)^3 i+(4)/(6)(3)^2 j =18 i +6 j

NEET 2002

Exam: NEET
Year: 2002
Subject: Physics
Chapter: Motion in One Dimension

NEET 2002 · Physics · Motion in One Dimension

An object of mass 3 ~kg is at rest. Now a force F=6 t^2 i +4 j is...

An object of mass

3 \mathrm{~kg}

is at rest. Now a force

F=6 t^2 \hat{i}+4 \hat{j}

is applied on the object then the velocity of the object at

t=3 \mathrm{~s}

is:

Options

A $18 \hat{i}+3 \hat{j}$
B $18 \hat{i}+6 \hat{j}$
C $3 \hat{i}+6 \hat{j}$
D $18 \hat{i}+4 \hat{j}$

Correct answer

B. $18 \hat{i}+6 \hat{j}$

Step-by-step solution

From question

\vec{a}=\frac{\vec{F}}{m}=2 t^2 \hat{i}+\frac{4}{3} t \hat{j}

\therefore d \vec{V}=\left(2 t^2 \hat{i}+\frac{4}{3} t \hat{j}\right) d t

Integrated both sides, We have,

\vec{V}=2\left[\frac{t^3}{3}\right] \hat{i}+\frac{4}{3}\left[\frac{t^2}{2}\right] \hat{j}

t=3 \mathrm{sec}, \vec{V}=\frac{2}{3}(3)^3 i+\frac{4}{6}(3)^2 j

=18 \hat{i}+6 \hat{j}

Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A vehicle runs on a straight road of length 'L'. It travels half the distance with speed… MHT CET Medical 2026 For uniform acceleration in linear motion which of the following is NOT CORRECT ? MHT CET Medical 2026 Two cars, P and Q move toward each other, getting 8\ m closer every second. If they move… MHT CET Medical 2026 A block is kept on the floor of an elevator at rest. The elevator starts descending with… MHT CET Medical 2026 The acceleration (a ) -time (t ) graph for the body starting from rest is as shown in the… MHT CET Medical 2026 A train accelerates from rest at a constant rate 'p' for some time (attains velocity 'v')… MHT CET Medical 2026 The following plots show variation of velocity ( v ) with time ( t ), of a ball thrown… NEET 2026 Consider a particle moving along a straight line, whose position as a function of time is… NEET 2026 Full Motion in One Dimension list All NEET PYQs