Question

A three wheeler starts from rest, accelerates uniformly with ` 1 ms^(-2)` on a straight road for ` 10 s` and then moves with uniform velocity. Plot a graph between the distance covered by the vehicle during the `n_(th)` second ( n = 1,2,3, ……..) versus n. What do you expect the plot to be during accelerated motion: a straight line or a parabola?
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Answer 1

Straight line
Distance covered by a body in `n^(th)` second is given by the relation
`D_n=u+a/2(2n-1)`…(i)
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=1/2(2n-1)` (ii)
This relation shows that:
`D_n prop n`...(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.