For a particle showing motion under the force $F = -5(x - 2)^2$,the motion is .......

$A$ train starts from rest from a station with acceleration $0.2 \, m/s^2$ on a straight track and then comes to rest after attaining maximum speed at another station due to retardation $0.4 \, m/s^2$. If the total time spent is half an hour,then the distance between the two stations is [Neglect the length of the train]. (in $, km$)

$A$ car travels from $A$ to $B$ (without changing direction). During the first part of the journey,its average speed is $V_1$,and for the second part of the journey,its average speed is $V_2$. The ratio of the path length of the second part to the path length of the first part is $\sqrt{\frac{V_2}{V_1}}$. In this case,the average speed of the total path is the ....... of the average speeds of both parts. Choose the correct option.

$A$ 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.

$A$ particle is constrained to move on a straight line path. It returns to the starting point after $10\, s$. The total distance covered by the particle during this time is $30\, m$. Which of the following statements about the motion of the particle is false?

$A$ man moves in an open field such that after moving $10 \, m$ on a straight line,he makes a sharp turn of $60^{\circ}$ to his left. The total displacement just at the start of the $8^{\text{th}}$ turn is equal to ........ $m$.