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# Uniform Motion

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 Sub Topics The Motion plays a key role in physics. It tells about changing position of a moving body for a given time. There are basically two types of motion:Uniform MotionNon uniform MotionIf the motion is consistent with time we use the term uniform motion. It happens when a body has constant speed in a straight line. Lets study more about this.

## What is Uniform Motion?

Let us see an illustration to understand the concept in a better way
A roller is rolling on a wooden log with constant speed as shown in figure. You could see that in 1st second it covers the same distance as that in 2nd second or so on. For any nth the distance traveled will be the same. This is what uniform speed concept tells us!
For any body moving in a straight line if it covers equal distance in equal intervals of time. Then the body is said to be in Uniform motion. It can be represented in graph

Uniform speed graph: It is plotted for displacement (d) versus time (t). Here we could observe for every 1 second there is displacement of 5m for any interval.

It shows the equal displacement in equal intervals of time. Hence the slope is given as

Uniform acceleration graph: It is plotted for velocity (v) versus time (t). The v-t graph for uniform motion gives the constant acceleration as shown below

## Equations of Motion

There are three equations of motions

Where v = Final velocity
u = Initial velocity
a = acceleration
t = time taken.

## Uniform Motion Problems

Here are given the few problems on uniform motion you can go through it:

### Solved Examples

Question 1: A bicycle is moving with a speed of 6 m/s is having an acceleration of 0.1 m/s2 comes to rest after 10 s. Calculate its final velocity.
Solution:

Given: Initial speed u = 6 m/s,
Acceleration a = 0.1 m/s2,
time taken t = 10 s

The Final velocity is given by
v = u + at
= 6 + 0.1 $\times$ 10
= 6 + 1 = 7 m/s.
The final velocity is 7 m/s.

Question 2: Joe is on the ride. He stops in the traffic. When signal turns green he accelerates his bike from rest at the rate of 4m/s2. What will be the displacement after 10s?
Solution:

Given: Initial velocity u = 0,
Acceleration a = 4 m/s2,
time taken t = 10 s
The displacement is given by
S = ut + $\frac{1}{2}$ at2

= 0 + $\frac{1}{2}$ $\times$ 4 $\times$ 102

= 0.5 $\times$ 4 $\times$ 100
= 200 m.

## Uniform Circular Motion

The uniform motion of a body in a circular path is uniform circular motion. When a body is moving in a circular path it changes its direction each time. At all the points in the path it will be tangent to the circle and will undergoing the uniform speed but varying acceleration.

Consider a body moving in uniform circular motion. At both points A and B the body moves with the constant speed.

## Uniform Circular Motion Examples

We come across many illustration of uniform circular motion in our daily life. Here are some:
• A merry going round with constant speed
• An athlete in race running in circular path maintaining consistent speed
• Artificial satellites moving around the earth.
• Earth moving round the sun.

## Uniform Circular Motion Problems

Let us go through some solved problems in uniform circular motion:

### Solved Examples

Question 1: A object of mass 3 kg is tied to the end of the rope of 5 m length. What will be its speed if it is whirled around uniformly for 2 min?
Solution:

Given : Mass of object m = 3 kg,
Length of rope r = 5m
time taken t = 2 min = 120 seconds
The distance is given by d = 2 $\pi$ r
= 2 $\times$ $\pi$ $\times$ 5m
= 31.42 m

The speed is given by S = $\frac{d}{t}$

= $\frac{31.42 m}{120 s}$

= 0.261 m/s.

Question 2: A car goes round in a circular track covering a distance of 100 m with a speed of 10 m/s. How much time will it take to do so?
Solution:

Given: Distance d = 100 m, speed s = 10 m/s,

The time taken is given by t = $\frac{d}{s}$

= $\frac{100 m}{10 m/s}$

= 10 s.