Question

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s=e^{t}(4\cos 3t+5\sin 3t)$. Then the velocity of the particle at time $t$ is given by

• A. $e^{t}(19\cos 3t-7\sin 3t)$
• B. $e^{t}(12\cos 3t-7\sin 3t)$
• C. $e^{t}(16\cos 3t+9\sin 3t)$
• D. $e^{t}(14\cos 3t-9\sin 3t)$
• E. $e^{t}(19\cos 3t+7\sin 3t)$

Hint:

Logic Tip: A massive time-saving rule: The derivative of $e^{at} \cdot f(t)$ is always $e^{at}[a \cdot f(t) + f'(t)]$. Here $a=1$, so you simply add the original function to its derivative: $(4\cos 3t + 5\sin 3t) + (-12\sin 3t + 15\cos 3t)$, getting $19\cos 3t - 7\sin 3t$ instantly.

Answer 1

The Correct Option is A