Question

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

• A. $3t^2+\cos t$
• B. $\frac{t^2}{2}+\sin t$
• C. $3t^2+\sin t$
• D. $\frac{t^2}{2}-\cos t$

Answer 1

The correct option is C $3t^2+\sin t$

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