Question

Velocity of a car as a function of time is given by $v\left(t\right)=(4t^3-e^t+\sin t)$ in $\text{m/s}$. The acceleration in $\left(m/s^2\right)$ of the car as a function of time $t$ is

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

Answer 1

The correct option is C $12t^2-e^t+\cos t$

As we know that the acceleration of the particle as a function of time is given by
$\frac{dv\left(t\right)}{dt}=\frac{d(4t^3-e^t+\sin t)}{dt}$
$\Rightarrow a\left(t\right)=12t^2-e^t+\cos t$