If s=et(sin⁡t−cos⁡t) is the equation of motion of a moving particle, then acceleration at time t is given by

A
$2 e^{t} (\cos t + \sin t)$
B
$2 e^{t} (\cos t - \sin t)$
C
$e^{t} (\cos t - \sin t)$
D
$e^{t} (\cos t + \sin t)$

Solution:

We have ,

$\begin{array}{l} s = e^{t} (\sin t - \cos t) \\ \Rightarrow \frac{d s}{d t} = 2 e^{t} \sin t \\ \Rightarrow \frac{d^{2} s}{d t^{2}} = 2 e^{t} (\sin t + \cos t) \end{array}$

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