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**.

- A car is moving at a constant speed of 10 m/s.
- The motion of the hands of a clock.
- The motion of the blades of a fan.
- 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**.

- The motion of a football during a game.
- The motion of a car on the road.
- Motion movement of living beings.
- 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 (t_{1}, d_{1}) and (t_{2}, d_{2}), respectively.

The slope of this graph is given by,

Slope, m = BC/ AC

Or **m = (d _{2} – d_{1})/ (t_{2} – t_{1}) = velocity**

[Slope from the position-time graph]

The velocity of the moving object is given by,

Or **m = (d _{2} – d_{1})/ (t_{2} – t_{1}) = 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**.

### Questions and Answers

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

**Answer: **Velocity

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

**Answer: **

- The position of a body at a certain time
- The velocity of a body
- The type of motion a body is undergoing
- The change in its velocity along its motion

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