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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 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 ?

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Straight line Distance covered by a body in nth second is given by the relation Where, u = Initial velocity a = Acceleration n = Time = 1, 2, 3, ..... ,n In the given case, u = 0 and a = 1 m/s2 This relation shows that: Dn ∝ n … (iii) Now, substituting different values of n in equation...
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Straight line

Distance covered by a body in nth second is given by the relation

Where,

u = Initial velocity

a = Acceleration

= Time = 1, 2, 3, ..... ,n

In the given case,

u = 0 and a = 1 m/s2

This relation shows that:

Dn ∝ … (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

Dn

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

8.5

9.5

The plot between and Dn 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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