For the velocity-time graph shown in the figure,the distance covered by the body in the last two seconds of its motion is $S_1$. What is the ratio of $S_1$ to the total distance covered by it?

Which of the following graphs represents uniform motion?

$A$ woman starts from her home at $9.00\; am$, walks with a speed of $5\; km\; h^{-1}$ on a straight road up to her office $2.5\; km$ away, stays at the office up to $5.00\; pm$, and returns home by an auto with a speed of $25\; km\; h^{-1}$. Choose suitable scales and plot the $x-t$ graph of her motion.

$Assertion$ : Velocity-time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis.
$Reason$ : In uniform motion of an object velocity increases as the square of time elapsed.

$A$ car starts from rest and travels with uniform acceleration $\alpha$ for some time and then with uniform retardation $\beta$ and comes to rest. If the total travel time of the car is $t$,the maximum velocity attained by it is given by:

$A$ particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = \beta x^{-2n}$,where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by: