Speed, velocity and acceleration

Welcome to the World of Motion!

Ever wondered how a GPS calculates your arrival time, or how an athlete knows exactly when to sprint? It all comes down to Kinematics—the study of how things move! Don't worry if Physics feels like a different language sometimes; we are going to break it down step-by-step. By the end of this chapter, you'll be able to describe any journey using just a few simple numbers and graphs.

1. Speed and Velocity: What's the Difference?

In everyday life, we use "speed" and "velocity" to mean the same thing. But in Physics, they are slightly different cousins!

Speed (A Scalar Quantity)

Speed only tells us how fast an object is moving. It doesn't care about the direction. If you are running at \( 5\text{ m/s} \), that is your speed.

\( \text{Average Speed} = \frac{\text{Total Distance Travelled}}{\text{Total Time Taken}} \)

Velocity (A Vector Quantity)

Velocity is "speed in a specific direction." It tells us how fast and which way. If you are running at \( 5\text{ m/s} \) towards the North, that is your velocity.

Memory Aid:
Speed is Scalar (Magnitude only)
Velocity is Vector (Magnitude + Direction)

Did you know?
If you run one full lap around a circular track and end up exactly where you started, your total distance might be \( 400\text{m} \), but your total displacement is zero! This means your average velocity for the whole trip would be \( 0\text{ m/s} \), even though you were running fast!

Key Takeaway: Use speed when direction doesn't matter; use velocity when you need to know where the object is heading.

2. Acceleration: Changing Gears

Acceleration is the rate at which velocity changes. If you speed up, slow down, or change direction, you are accelerating!

Uniform Acceleration

This is when the velocity of an object changes by the same amount every second. For example, if a car increases its speed by \( 2\text{ m/s} \) every single second, it has a uniform acceleration of \( 2\text{ m/s}^2 \).

How to calculate it:
\( \text{Acceleration} (a) = \frac{\text{Change in Velocity}}{\text{Time Taken}} = \frac{v - u}{t} \)
Where:
\( v \) = Final velocity
\( u \) = Initial (starting) velocity
\( t \) = Time taken

Non-Uniform Acceleration

In the real world, acceleration often changes. If you press the gas pedal harder and harder, your acceleration is increasing. If you see a curve on a velocity-time graph, that’s a sign of non-uniform acceleration.

Quick Review:
- Positive acceleration: Speeding up.
- Negative acceleration (Deceleration): Slowing down.
- Zero acceleration: Moving at a constant speed in a straight line.

3. Mastering Motion Graphs

Graphs are like "pictures" of a journey. There are two main types you need to know. Don't worry if they look confusing at first—just look at what the gradient (slope) represents!

Type A: Displacement-Time (s-t) Graphs

These show how far an object is from its starting point over time.

• Horizontal flat line: The object is at rest (stopped).
• Straight sloped line: The object is moving with uniform (constant) velocity.
• Curved line: The object is moving with non-uniform velocity (it is accelerating or decelerating).

Pro Tip: The gradient of a displacement-time graph = Velocity.

Type B: Velocity-Time (v-t) Graphs

These show how the speed of an object changes over time.

• Horizontal line on the x-axis: The object is at rest.
• Horizontal line above the x-axis: The object is moving with uniform velocity (acceleration is zero).
• Straight sloped line: The object is moving with uniform acceleration.
• Curved line: The object is moving with non-uniform acceleration.

The "Magic" of v-t Graphs:
1. The gradient of a v-t graph = Acceleration.
2. The area under a v-t graph = Displacement (distance travelled).

Common Mistake to Avoid:
Students often confuse the two graphs. Always check the labels on the axes! If the vertical axis is Displacement, a flat line means "stopped." If the vertical axis is Velocity, a flat line means "constant speed."

4. Free Fall: Gravity in Action

When you drop an object, it falls because of gravity. If we ignore air resistance, all objects fall with the same constant acceleration near the Earth's surface.

The Magic Number: \( 10\text{ m/s}^2 \)

In the O-Level syllabus, the acceleration of free fall (represented by \( g \)) is approximately \( 10\text{ m/s}^2 \).

What does this actually mean?
If you drop a ball from a tall building:
- After 1 second, it's falling at \( 10\text{ m/s} \).
- After 2 seconds, it's falling at \( 20\text{ m/s} \).
- After 3 seconds, it's falling at \( 30\text{ m/s} \).
It gains \( 10\text{ m/s} \) of speed every second!

Key Takeaway: Unless the question mentions air resistance, always assume an object in free fall accelerates downwards at a constant rate of \( 10\text{ m/s}^2 \).

Summary Checklist

Before you move on, make sure you can:
- [ ] Explain why velocity is a vector but speed is a scalar.
- [ ] Use the formula \( \text{Average speed} = \frac{\text{Total Distance}}{\text{Total Time}} \).
- [ ] Calculate acceleration using \( \frac{v-u}{t} \).
- [ ] Identify "rest," "constant velocity," and "acceleration" on both s-t and v-t graphs.
- [ ] Find the distance travelled by calculating the area under a v-t graph.
- [ ] State that free-fall acceleration is \( 10\text{ m/s}^2 \).

You've got this! Kinematics is the foundation for everything else in Physics. Keep practicing those graph interpretations and you'll be a pro in no time!