In what different ways can the velocity of an object be changed?

The $v-t$ graph of an object of mass $1\,\text{kg}$ is shown. Which of the following statements is correct?

$A$ particle starts moving from time $t=0$ and its coordinate is given as $x(t)=4t^{3}-3t.$ Which of the following statements are correct?
$A$. The particle returns to its original position (origin) at $t = \frac{\sqrt{3}}{2} \approx 0.866$ units later.
$B$. The particle is $1$ unit away from the origin at its turning point.
$C$. Acceleration of the particle is non-negative for $t \ge 0$.
$D$. The particle is $0.5$ units away from the origin at its turning point.
$E$. The particle never turns back as acceleration is non-negative.

Choose the correct statement.

At time $t=0$, a particle leaves the origin and moves in the positive direction of the $X$-axis. If the velocity of the particle varies as $v(t)=v_0(1-t/t_0)$, where $|v_0|=10 \ m/s$ and $t_0=10 \ s$, then the distance covered by the particle during the first $20 \ s$ is: (in $m$)

$A$ car accelerates from rest with $2 \,m/s^2$ on a straight line path and then comes to rest after applying brakes. Total distance travelled by the car is $100 \,m$ in $20 \,s$. Then, the maximum velocity attained by the car is (in $\,m/s$)