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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

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    $\begingroup$ Why are you unsure? $\endgroup$
    – Bob D
    Commented Feb 22, 2021 at 12:36
  • $\begingroup$ Are there any equations that could explain it better than I had? $\endgroup$
    – snowyman01
    Commented Feb 22, 2021 at 12:38
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    $\begingroup$ So what is the effect of $u$? $\endgroup$
    – Gert
    Commented Feb 22, 2021 at 12:41
  • $\begingroup$ 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) $\endgroup$
    – snowyman01
    Commented Feb 22, 2021 at 12:45
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    $\begingroup$ Your equation is basic kinematics, and your conclusion is correct. $\endgroup$
    – Bob D
    Commented Feb 22, 2021 at 12:52

2 Answers 2

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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.

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The initial velocities matters, but direction of acceleration would also effect the overall distanced traveled. For example, objects (with the same initial velocities) accelerated in opposite directions could increase the velocity of one object and decrease the velocity of the other. Obviously their distanced traveled would be different.

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