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 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?
Straight line
Distance covered by a body in $n^{\text {th }}$ second is given by the relation $D_{n}=u+\frac{a}{2}(2 n-1)\ldots(i)$
Where,
$u=$ Initial velocity
$a=$ Acceleration
$n=$ Time $=1,2,3, \ldots \ldots, n$
In the given case, $u=0$ and $a=1 m / s ^{2}$
$\therefore D_{n}=\frac{1}{2}(2 n-1)\dots (ii)$
This relation shows that
$D_{n} \propto n \ldots (iii)$
Now, substituting different values of $n$ in equation (iii), we get the following table
| $n$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
| $D_n$ | $0.5$ | $1.5$ | $2.5$ | $3.5$ | $4.5$ | $5.5$ | $6.5$ | $7.5$ | $8.5$ | $9.5$ |
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 $n=10 s$
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