rectilinear motion

please help with question 5, thank you.

(a)

$\begin{array}{rcll} s(t) &=& \sin{(e^t)} \\\\ v(t) &=& s'(t) \\ v(t) &=& \cos{(e^t)}\cdot e^t \\ \mathbf{ v(t) }& \mathbf{=} & \mathbf{e^t \cdot \cos{(e^t)} } \\\\ a(t) &=& v'(t) \\ a(t) &=& e^t \cdot [ -\sin{(e^t)}\cdot e^t ] + e^t\cdot \cos{(e^t)} \\ \mathbf{a(t) }&\mathbf{=} &\mathbf{ e^t \cdot [ \cos{(e^t)} - e^t\cdot\sin{(e^t)} ] }\\ \end{array}$

(b)

$\begin{array}{rcll} \mathbf{ v(t) }& \mathbf{=} & \mathbf{e^t \cdot \cos{(e^t)} } \\\\ 0 & = & \underbrace{e^t}_{=0\ \text{ impossible} } \cdot \underbrace{ \cos{(e^t)} }_{=0} \\ \cos{(e^t)} &= & 0 \qquad & | \qquad \arccos{()}\\ e^t &= & \arccos{(0)}\\ e^t &= & \frac{\pi}{2} \qquad & | \qquad \ln{()}\\ \ln{( e^t )} &= & \ln{(\frac{\pi}{2})} \\ t \cdot \ln{( e )} &= & \ln{(\frac{\pi}{2})} \qquad & | \qquad \ln{(e)} = 1\\ t &= & \ln{(\frac{\pi}{2})} \\ \mathbf{ t } & \mathbf{=} & \mathbf{0.45158270529\ \text{ seconds} }\\ \end{array}$

(c)

$\begin{array}{rcll} \mathbf{a(t) }&\mathbf{=} &\mathbf{ e^t \cdot [ \cos{(e^t)} - e^t\cdot\sin{(e^t)} ] }\qquad & | \qquad t = 0.45158270529\ \text{ seconds}\\ a(0.45158270529) & = & e^t \cdot [ \cos{(e^t)} - e^t\cdot\sin{(e^t)} ] \qquad & | \qquad e^t = \frac{\pi}{2}\\ a(0.45158270529) & = & \frac{\pi}{2} \cdot [ \cos{(\frac{\pi}{2})} - \frac{\pi}{2}\cdot \sin{(\frac{\pi}{2})} ] \qquad & | \qquad \sin{(\frac{\pi}{2})} = 1\\ a(0.45158270529) & = & \frac{\pi}{2} \cdot [ \cos{(\frac{\pi}{2})} - \frac{\pi}{2}\cdot 1 ] \qquad & | \qquad \cos{(\frac{\pi}{2})} = 0\\ a(0.45158270529) & = & \frac{\pi}{2} \cdot [ 0 - \frac{\pi}{2}\cdot 1 ] \qquad & | \qquad \cos{(\frac{\pi}{2})} = 0\\ a(0.45158270529) & = & \frac{\pi}{2} \cdot ( - \frac{\pi}{2} ) \\ a(0.45158270529) & = & - \frac{\pi}{2} \cdot \frac{\pi}{2} \\ a(0.45158270529) & = & - \frac{\pi^2}{4}\\ \mathbf{ a(0.45158270529) }& \mathbf{=} & \mathbf{ - 2.46740110027\ \frac{\text{feet}}{ \text{second} } }\\ \end{array}$

it seems to b ur home work problem..  ill just say the method. for ques (a) just differentiate displacement equation for velocity and double differentiate for acceleration. for ques (b) substitute velocity=0 in velocity eqn. found in previous ques. for ques (c) subs the time found in (b) in eqn. of velocity n acc. in (a).