A three-wheeler starts from rest, accelerates uniformly with `1 ms^(-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 ?

Explanation

Here u = 0, a = 1 `m//s^(2)`
Distance covered in n th second is
`D_(n)=u+a/2(2n-1)=0+1/2(2n-1)=0.5(2n-1)`
Putting n = 1, 2, 3, ……….., we can find the value of `D_(n)`. The various values of n and corresponding values of `D_(n)` are shown below :

On plotting a graph between `D_(n) and n`, we get a st. line AB as shown in fig. From (1) `D_(n)propto_(n)` so the graph is straight line. After 10S the graph is straight line BC parallel to time axis.