All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

$A$ 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.

Which of the following four statements is false?

Assertion $(A)$: The angle between acceleration and velocity of a body in one-dimensional motion is always zero. Reason $(R)$: One-dimensional motion is along a straight line.

$A$ cyclist starts from the centre $O$ of a circular park of radius $1\; km$,reaches the edge $P$ of the park,then cycles along the circumference,and returns to the centre along $QO$ as shown in Figure. If the round trip takes $10 \;min$,what is the
$(a)$ net displacement,
$(b)$ average velocity,and
$(c)$ average speed of the cyclist?

The engine of a motorcycle can produce a maximum acceleration $5 \, m/s^2$. Its brakes can produce a maximum retardation $10 \, m/s^2$. What is the minimum time in which it can cover a distance of $1.5 \, km$?