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

Initial velocity `u = 0 ms ^(-1)`
Acceleration `a = 1 ms ^(-2)`
Time `t = 10s `
Distance covered in `n^(th)` second,
`S_(n) = u + (a)/(2) (2n -1)` [where t = n]
`therefore S _(n) = a/2 (2n-1)" "…(1)`
For `n =1, S_(1)= 1/2 (2-1) =1/2 =0.5m`
For `n = 2, S_(2) = 1/2 (4-1) = 3/2 = 1.5m`
For `n = 3, S_(3) = 1/2 (6-1) = 5/2 = 2.5m`
Similary,
For `n = 4, S_(4)=3.5m`
For `n = 5, S _(5) =4.5m`
For `n = 6, S_(6) = 5.5m`
For `n = 6, S_(7)=6.5m`
For `n = 8, S_(8)=7.5m`
For `n = 9, S_(9) =8.5 m`
For `n = 10, S_(10) = 9.5m`

`S_(n) to t` graph will be AB a straight line.
After 10 s, graph will be parallel to .t. axis like BC.