Answer
(a) When velocity of the particle is zero-
At $t=0 \Rightarrow Position \space x=2.17 \space m$ and $Acceleration\space a=9.60 \space m/s^2$
At $t=2\space s \Rightarrow Position \space x=2.17+4.80\times 2^2-0.100\times 2^6\approx 15 \space m$ and $Acceleration\space a=9.60-3.00\times 2^4=-38.4 \space m/s^2$
(b) Plot for position, velocity and acceleration as a function of time, will be as shown in figure-
Work Step by Step
(a) Velocity of the particle at time t, $v_x(t)=\frac{dx(t)}{dt}=9.60t-0.600t^5\space (m/s)$
Acceleration of the particle at time t, $a_x(t)=\frac{dv_x}{dt}=9.60-3.00t^4\space (m/s^2)$
For velocity of the particle to be zero-
$v_x=9.60t-0.60t^5=0\Rightarrow t=0\space and \space t=\frac{96}{6}^{1/4}=2 \space s$
So, when velocity of the particle is zero-
At $t=0 \Rightarrow Position \space x=2.17 \space m$ and $Acceleration\space a=9.60 \space m/s^2$
At $t=2\space s \Rightarrow Position \space x=2.17+4.80\times 2^2-0.100\times 2^6\approx 15 \space m$ and $Acceleration\space a=9.60-3.00\times 2^4=-38.4 \space m/s^2$
(b) Plot for position, velocity and acceleration as a function of time, will be as shown in figure-
