# Comparison Between Uniform And Non-Uniform Motion

If we analyze our motion from home to office we can visualize that we are not moving with a constant velocity all the time. Sometimes we are moving at a higher velocity, while at other times like in crowded places like markets the velocity will be less. But we can always define an average velocity for the motion. Based on this we can classify the motion to be uniform or non-uniform.

### Uniform Motion:

In an uniform motion the body covers equal distances in equal interval of time. That means it has a constant velocity over the given period of time. By looking at the x – t and v – t graph we can say what kind of motion it is. First we will take x – t graph:

From the graph we can see that the slope is constant. Therefore,

$\frac{Change ~in ~displacement}{Change~ in ~time}$ = $Constant$

So the motion is uniform. Similarly if we take a v – t graph and the plot is horizontal or parallel to time axis then the motion is uniform as it cover equal distance in equal interval of time.

### Non uniform motion:

As the name suggests that a motion in which body covers unequal distances in equal intervals of time is known as a non – uniform motion. Let’s see the following v – t graph:

We know are under v – t graph represents displacement of the body. As we can see for same time interval the area under A and B are different. So this is a non – uniform motion. So with respect to non–uniform motion we usually define average velocity. The average velocity formula is:

$Average ~Velocity$ = $\frac{Change~ in ~displacement}{Time~ Taken}$

From the equation of motion,

$Displacement$ = $ut ~+~\frac{1}{2}at^2$

$Average~ Velocity$ = $\frac{ut ~+ ~\frac{1}{2} at^2}{t}$

= $u ~+~\frac{at}{2}$

From first equation of motion,

$Average~ velocity$ = $u ~+~ \frac{v ~-~ u}{2}$

$Average~ Velocity$ = $\frac{v~+~ u}{2}$

Where, $v$ = Final Velocity

$u$ = Initial Velocity

Similarly we can define average speed. The formula for average speed is given us:

$Average~ speed$ = $\frac{Change~ in~ distance}{Time~ Taken}$

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