❓ How fast is an object moving?
❓ How does its velocity change?

The answers to these two questions lead us to two concepts: Velocity and Acceleration.

🚗 What Is Velocity?

Velocity tells us how much and in which direction an object's position changes.
The formula for average velocity is:
v = Δx / Δt
where:
v → velocity
Δx → change in position or displacement
Δt → change in time

The SI unit of velocity is:
m/s
For example, if a car moves 50 meters east in 10 seconds:
v = 50 / 10
v = 5 m/s east

🔵 Average Velocity and Instantaneous Velocity

We have two important concepts:

Average Velocity

Average velocity is calculated over a specific time interval.

v_avg = Δx / Δt

But:

Instantaneous Velocity

Instantaneous velocity describes the velocity of an object at a specific moment.
For example, the speedometer of a car approximately shows the car's instantaneous velocity.

⚡ What Is Acceleration?

If an object's velocity changes, the object has acceleration.

The formula for average acceleration is:
a = Δv / Δt
where:

a → acceleration
Δv → change in velocity
Δt → change in time

The SI unit of acceleration is:

m/s²

🚘 A Simple Example

Suppose the velocity of a car increases from:
10 m/s
to:
30 m/s
over:
5 s
Therefore:
a = (30 − 10) / 5
a = 20 / 5
a = 4 m/s²

This means that, on average, the car's velocity increases by 4 m/s every second.

🧠 What Is Negative Acceleration?

If an object's velocity decreases, its acceleration can be in the opposite direction of its motion.
For example, if a car's velocity decreases from:

20 m/s
to:
10 m/s
over:
5 s
then:
a = (10 − 20) / 5
a = −2 m/s²

The negative sign indicates that the change in velocity is in the negative direction of the chosen axis.

Therefore:

Negative acceleration does not always mean "slowing down."
The direction of motion and the direction of acceleration must be considered together.

📊 Position–Time Graph

One important way to study motion is by using graphs.

In a position–time graph:

Vertical axis → position x

Horizontal axis → time t

The slope of a position–time graph represents velocity.

Slope = Δx / Δt = v

Therefore:

📈 Greater slope → Greater velocity
📉 Smaller slope → Smaller velocity
➖ Horizontal line → Object is at rest

📈 Velocity–Time Graph

In a velocity–time graph:

Vertical axis → velocity v

Horizontal axis → time t

The slope of a velocity–time graph represents acceleration.

Slope = Δv / Δt = a

Therefore:

📈 Positive slope → Positive acceleration
📉 Negative slope → Negative acceleration
➖ Horizontal line → Constant velocity

💡 Connection to Optics

Velocity and acceleration are not only used for cars and everyday objects.

In physics, the concept of velocity is very important for studying the propagation of waves and light.

The speed of light in vacuum is:
c ≈ 3 × 10⁸ m/s

However, when light enters a medium such as glass or water, its propagation speed decreases.
Later, we will see that the speed of light in a medium is related to the refractive index (n):
v = c / n

This relationship is one of the important steps on our journey into optics and the refraction of light. 💡

🧪 Today's Exercise

A car is moving with a velocity of:

10 m/s
After 5 seconds, its velocity reaches:
25 m/s

❓ What is the average acceleration of the car?

Use the following equation:

a = Δv / Δt

👨‍🔬 Scientist of the Day

Ole Rømer

Ole Rømer, a Danish astronomer, was one of the first scientists to show that the speed of light is finite and that light travels at an extremely high, but not infinite, speed.


Optics & Lasers | University of Bonab
The Science of Light Starts Here.

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