$A$ particle moves along a straight line such that its retardation is proportional to its displacement. The loss in its kinetic energy for any displacement $x$ is proportional to:

Which of the following curves possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given below.

$Assertion$: $A$ body with constant acceleration always moves along a straight line.
$Reason$: $A$ body with constant acceleration may not speed up.

Two masses of $3.4 \text{ kg}$ and $2.5 \text{ kg}$ are accelerated from an initial speed of $5 \text{ m/s}$ and $12 \text{ m/s}$, respectively. The distances traversed by the masses in the $5^{th}$ second are $104 \text{ m}$ and $129 \text{ m}$, respectively. The ratio of their momenta after $10 \text{ s}$ is $\frac{x}{8}$. The value of $x$ is . . . . . . .

Two cars start from a point at the same time in a straight line and their positions are represented by $x_1(t) = at + bt^2$ and $x_2(t) = Ft - t^2$. At what time do the cars have the same velocity?

$A$ particle moves along the straight line $y=3x+5$. Which coordinate changes at a faster rate?