Question

An object of mass $2kg$ at rest an origin starts moving under the action of a force
$\overrightarrow{F}=(3t^2\hat{i}+4t\hat{j})N$
The velocity of the object at $t=2s$ will be ?

• A. $(3\hat{i}+2\hat{j})m/s$
• B. $(2\hat{i}+4\hat{j})m/s$
• C. $(4\hat{i}+4\hat{j})m/s$
• D. $(3\hat{i}-4\hat{j})m/s$

Answer 1

The correct option is C $(4\hat{i}+4\hat{j})m/s$

Given data

$M=2kg$

$F=(3t^{2}i+4tj)N$

we know that $F=ma$

$=m\frac{dv}{dt}[\because a=\frac{dv}{dt}]$

integrating on both side

$\int Fdt=m\int du$

$\int Fdt=mv$

$\int (3t^{2}i+4tj)dt=2v$

$\frac{3t^{3}i}{3}+\frac{4t^2}{2}j=2v$

$t^{3}i+2t^{2}j=2v$

substituting t22

$8i+8j=2v$

$\therefore v=(4i+4j)m/s$

$AnswerisC$