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### Motion in a straight line NCERT Solutions Class 11 Physics - Solved Exercise Question 3.23

Question 3.23

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 ?

Solution:

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:
Dnn … (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.