A three-wheeler starts from rest, accelerates uniformly with 1 m/s^{2} on a straight road for 10 s ,

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2.Motion in Straight Line

medium

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?

Option A

Option B

Option C

Option D

Solution

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 $n=10 s$

Standard 11

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