Question

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?

Answer 1

Initial velocity u = 0.

Acceleration a = 1 ms^-2.

Acceleration time = 10 s

Let s_n be the total displacement (or distance in this case) in time ‘n’ seconds.

s_n = ut + 1/2 at²

s_n = 0(n) + 1/2 a(n²) = 1/2 an² for n ≤ 10

Distance covered in ‘n’^th second d_n = s_n – s_n – 1

= 1/2 an² – 1/2 a(n - 1)²

= an – 1/2 a(for n ≤ 10)

= (n – 1/2)m

At the end of 10 seconds, velocity acquired v = u + at = 0 + a(10) 10 a = 10 ms^-1

Distance covered in the ‘n’^th second = 10m for n >10

∴ d_n = {(n-1/2)m n ≤ 10,

10m n > 10

The plot is a straight line inclined to the time axis for uniformly accelerated motion. (It is a straight line parallel to the time axis for uniform motion).