Question

Velocity of a car as a function of time is given by $v\left(t\right)=(4t^3+e^t)$ in $\text{m/s}$. The displacement in $\left(m\right)$ of the car as a function of time $t$ is

• A. $4t^2+e^t$
• B. $t^4+e^t$
• C. $12t^2+e^t$
• D. $t^4-e^t$

Answer 1

The correct option is B $t^4+e^t$

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