Question

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

Answer 1

Straight line
Distance covered by a body in $n^{th}$ second is given by the relation
$D_n=u+\frac{a}{2}(2n-1)\dots \left(i\right)$
Where,
u = Initial velocity
a = Acceleration
n = Time = 1, 2, 3, ..... , n
In the given case, u = 0 and $a=1m/s^2$
$\therefore D_n=\frac{1}{2}(2n-1)\dots \left(ii\right)$
This relation shows that:
$D_n\propto n\dots \left(iii\right)$
Now, substituting different values of n in equation (iii), we get the following table:
$\begin{array}{ccccccccccc}n& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ D_n& 0.5& 1.5& 2.5& 3.5& 4.5& 5.5& 6.5& 7.5& 8.5& 9.5\end{array}$
The plot between n and $D_n$ will be a straight line as shown:


Since the given three-wheeler acquires uniform velocity after 10 s, the line will be parallel to the time-axis after n = 10 s.