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# Velocity – Constant, Average and Instantaneous Velocity

May 7, 2023

In this session, we will look at the terms such as speed, velocity, uniform, non-uniform motion, position-time graphs, etc. We will also calculate the velocity of a moving body from its position-time graphs.

## Speed and Velocity

The measure of fastness of the motion of a body is called its Speed. Speed can be measured in the units of km/h, m/s, miles/h, etc. The SI unit of speed is m/s.

The speed of an object moving in a specific direction is called Velocity.

The velocity of a body changes when there is a change in the speed, direction, or both.

Mathematically,

Velocity, v = displacement/ time taken

For a body traveling in a straight line,

Speed + Direction = Velocity

Its SI unit of measurement is also “m/s.”

### Velocity:

Velocity not only describes how fast an object moves from one position to another but also indicates the direction in which the object is moving.

It is defined as the rate of change of position of an object.

## Velocity

Velocity is the quotient of displacement and the time interval.

## Uniform and Non-Uniform Motion

A body that covers equal distances in equal intervals of time is said to be in a uniform motion.

1. A car is moving at a constant speed of 10 m/s.
2. The motion of the hands of a clock.
3. The motion of the blades of a fan.
4. The motion of a cruising jet.

A body that covers unequal distances in equal intervals of time is said to be in a non-uniform motion.

1. The motion of a football during a game.
2. The motion of a car on the road.
3. Motion movement of living beings.
4. The motion of a space shuttle during lift-off.

### Position-time Graph

To identify whether a motion is uniform or not, one needs to note the timestamps against the velocities of a moving object, as shown in the table.

The next step is to plot the position of the object against the timestamps and analyze the graph.

This graph is called the position-time graph.

If the position-time graph for a particular motion turns out to be a straight line with an upward (positive) slope, the motion of that body is uniform.

### Significance of the Position-time Graph

The slope of the position-time graph is given below.

The slope is a measure of the steepness of a graph.

In the adjacent distance-time graph, let the coordinates of A and B be (t1, d1) and (t2, d2), respectively.

The slope of this graph is given by,

Slope, m = BC/ AC

Or m = (d2 – d1)/ (t2 – t1) = velocity

[Slope from the position-time graph]

The velocity of the moving object is given by,

Or m = (d2 – d1)/ (t2 – t1) = velocity

Thus, velocity = (1750 – 350)/ (150 – 30)

Velocity = 1400/120

Velocity = 11.66 m/s[E]

### Types of Position-time Graphs:

Position-time graph of a body in a uniform motion at a negative velocity:

An object’s velocity can be considered to be negative when it moves in the opposite direction w.r.t its initial direction of motion. The slope of the position-time graph of a body in uniform motion at a negative velocity is negative. The adjacent graph is the s-t graph of a body moving at a constant negative velocity.

### Position-time Graph of a Body at Rest

The displacement of a body at rest does not change with time.

The displacement of a body at rest does not change with time. Therefore, the s-t graph of a body at rest is a straight line parallel to the x (time)- axis. The slope of this graph is zero, as it is parallel to the x-axis. That indicates the velocity of the body is zero.

1. The slope of a position-time graph refers to the _______ of a moving body.

1. What is the information that we can get from a position-time graph of a moving body?

1. The position of a body at a certain time
2. The velocity of a body
3. The type of motion a body is undergoing
4. The change in its velocity along its motion

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