## 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? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-3 Motion In A Straight Line

### 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 ?

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
= 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 ∝ … (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 shown in below figure: