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
Similarly, total distance travelled in n - 1 second would be Sn-1
Distance travelled in nth second would be given as
xn = Sn - Sn-1
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.