Q.23: A threewheeler 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 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:
Straight line
Distance covered by a body in n^{th} second is given by the relation
D_{n} = u + a (2n – 1)/2 ….(i)
Where,
u = Initial velocity
a = Acceleration
n = Time = 1, 2, 3, ….. ,n
In the given case,
u = 0 and a = 1 m/s^{2}
∴ D_{n} = (2n – 1) / 2 ….. (ii)
This relation shows that:
D_{n} ∝ 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 shown in below figure: