Question

for accelerated motion, how do changes in distance compare with equal changes in time?

Answer 1

Consider an object starts from rest and moving with constant acceleration.

from equations of motion:

Here v₀ is the initial velocity, a is the acceleration and t is the time.

since starts from rest, v₀ = 0, thus

thus, for constant acceleration the distance is directly proportional to the square of the time.

Therefore, the distance changes for first second, in first 2seconds, first 3seconds like,

x₁: x₂ : x₃ : x₄ = 1 : 4 : 9 :25

For equal changes in time, like first second, only in 2second, only in 3sec,.... the object traveled equal distances.