Question

Velocity of a car as a function of time is given by $v\left(t\right)=(3t^3-\sin t)$ in $\text{m/s}$. The displacement in $\left(m\right)$ of the car as a function of time $t$ is
[Take $x=0$ at $t=0$]

• A. $(\frac{3t^4}{4}-\cos t)$
• B. $9t^2-\cos t$
• C. $9t^2+\cos t$
• D. $(\frac{3t^4}{4}+\cos t)$

Answer 1

The correct option is D $(\frac{3t^4}{4}+\cos t)$

As we know that the displacement of the particle as a function of time is given by
$x\left(t\right)={\int }_0^{t}v\left(t\right)dt={\int }_0^t(3t^3-\sin t)dt$
$\Rightarrow x\left(t\right)=(\frac{3t^4}{4}+\cos t)\text{m}$