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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 ?
Asked by Bhupen Last Modified
Answer 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 (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 n 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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