# How are acceleration, time and velocity related?

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Sep 22, 2015

Time is the medium for both velocity and acceleration to occur. In a certain amount of time, an object will have moved a certain distance- This distance is defined by the velocity or acceleration.

Let's start by understanding velocity. Velocity is defined by as the rate of change of an object's displacement over its change in time (with direction, since velocity is a vector- that's why velocity can be negative). Basically, it just means "how much has this object moved (and in what direction) in a given time interval."

Acceleration is a little more complicated. It is defined as the rate of change of the object's velocity over its change in time. So "how much has the object's velocity changed in a given time interval." That's why when people think of acceleration, they think about things speeding up. Or, if the acceleration is negative, it's called deceleration and describes something slowing down. For something to speed up or slow down, it has to have a certain change in velocity.

Let's compare the units of the two. Velocity has the SI units of meters/second, which makes sense, because it's moving a certain amount of distance per a certain amount of time. Acceleration has units of meters/secondsquared. This just means that it's not always moving the same distance in a given time. If the acceleration is positive, it's actually moving more distance as time passes by.

Another relationship between the two is that when velocity is constant, acceleration is zero. Why? Because, since acceleration is defined as the change in velocity, and there is no change in velocity, the acceleration is actually zero. You can see all of these comparisons in this graph (if you don't know calculus yet, you can just focus on the diagram)-

http://hyperphysics.phy-astr.gsu.edu/hbase/acons.html

Also, when the acceleration is constant, the three variables are related to each other with the following equation:

$v = u + a t$

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