Q.23:- 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 ?
Answer:-
Straight line
Distance covered by a body in nth second is given by the relation
Dn = 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/s2
∴ Dn = (2n – 1) / 2 ….. (ii)
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 shown in below figure:
