Question

The position of the particle is given by $x=(e^t-\cos t)$ in $\text{m}$. The velocity $\left(\text{in m/s}\right)$ of the particle as a function of time $t$ is

• A. $e^t-\sin t$
• B. $e^t-\sec t$
• C. $e^t+\tan t$
• D. $e^t+\sin t$

Answer 1

The correct option is D $e^t+\sin t$

As we know that the velocity of the particle as a function of time is given by
$\frac{dx}{dt}=\frac{d(e^t-\cos t)}{dt}$
$\Rightarrow v=e^t+\sin t$