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.

$A$ particle has an initial velocity of $10 \, m/s$. It moves due to a constant retarding force along the line of motion,which produces a retardation of $5 \, m/s^2$. Then:

$A$ particle moving along a straight line covers the first half of the distance with a speed of $3 \, m \, s^{-1}$. The other half of the distance is covered in two equal time intervals with speeds of $4.5 \, m \, s^{-1}$ and $7.5 \, m \, s^{-1}$ respectively. The average speed of the particle during the motion is:

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

Two stones are thrown up simultaneously from the edge of a cliff $240 \ m$ high with initial speeds of $10 \ m/s$ and $40 \ m/s$ respectively. Which of the following graphs best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance,take $g = 10 \ m/s^2$)

$A$ 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.