# Does two objects are moving at the same time with the same acceleration, have the same distance travelled? [closed]

If two objects are moving at the same time with the same acceleration, would they have the same distance travelled?

I used this formula to explain that it depends on the initial velocity of the objects but I am not sure if I am right.

$$s = ut + ½ at^2$$ where, $$u$$ = initial velocity, $$a$$ = acceleration, $$t$$ = time taken, $$s$$ = displacement.

note: the situation is for rectilinear motion only

• Why are you unsure? Commented Feb 22, 2021 at 12:36
• Are there any equations that could explain it better than I had? Commented Feb 22, 2021 at 12:38
• So what is the effect of $u$?
– Gert
Commented Feb 22, 2021 at 12:41
• u is the initial velocity, so for two objects to travel the same distance, with the same acceleration and in the same time frame, they both have to have the same initial velocity (or so I think) Commented Feb 22, 2021 at 12:45
• Your equation is basic kinematics, and your conclusion is correct. Commented Feb 22, 2021 at 12:52

It depends on whether they have the same initial velocity $$u$$ or not.
In the affirmative case, both objects share the same equation for the distance traveled $$s=ut+1/2at^2$$.
In the negative case ($$u_1 \neq u_2$$), you have a different equation for the distance traveled for each object.