# Q 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?

Initial velocity u = 0

Acceleration, a = 1 ms-2

t = n seconds

Let the total distance travelled in n seconds be Sn

$\\S_{n}=ut+\frac{1}{2}at^{2}\\ S_{n}=0\times n+\frac{1}{2}\times 1\times n^{2}\\ S_{n}=\frac{n^{2}}{2}$

Similarly, total distance travelled in n - 1 second would be Sn-1

$\\S_{n-1}=\frac{(n-1)^{2}}{2}$

Distance travelled in nth second would be given as

x= Sn - Sn-1

$\\x_{n}=\frac{n^{2}}{2}-\frac{(n-1)^{2}}{2}\\ x_{n}=n-\frac{1}{2}$

As we can see the dependency of xn on n is linear we conclude the plot of the distance covered by the vehicle during the nth second versus n would be a straight line.

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