$A$ three-wheeler starts from rest,accelerates uniformly with $1\; m/s^{2}$ on a straight road for $10\; s$,and then moves with uniform velocity. Plot the distance covered by the vehicle during the $n^{\text{th}}$ second $(n = 1, 2, 3, \ldots)$ versus $n$. What do you expect this plot to be during accelerated motion: a straight line or a parabola?

(A) The plot is a straight line.
The distance covered by a body in the $n^{\text{th}}$ second is given by the formula:
$D_{n} = u + \frac{a}{2}(2n - 1) \quad \dots(i)$
Where:
$u = \text{Initial velocity}$
$a = \text{Acceleration}$
$n = \text{Time interval in seconds}$
In the given case,$u = 0$ and $a = 1\; m/s^{2}$. Substituting these values into equation $(i)$:
$D_{n} = 0 + \frac{1}{2}(2n - 1) = n - 0.5$
This relation $D_{n} = n - 0.5$ shows that $D_{n}$ is a linear function of $n$. Therefore,the plot of $D_{n}$ versus $n$ is a straight line.
Substituting different values of $n$ from $1$ to $10$:

$n$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$D_{n}$	$0.5$	$1.5$	$2.5$	$3.5$	$4.5$	$5.5$	$6.5$	$7.5$	$8.5$	$9.5$

Since the three-wheeler moves with uniform velocity after $10\; s$,the acceleration becomes zero. For $n > 10$,the distance covered in each subsequent second remains constant,so the plot becomes a horizontal line parallel to the $n$-axis.