Welcome to the World of Motion!
Welcome to Kinematics! This is often the first chapter students dive into for AS Level Physics. Don't let the name intimidate you—kinematics is simply the study of how things move. We aren't worried about why they move (that’s for the next chapter on Dynamics); we just want to describe their journey using numbers, graphs, and equations.
Whether you are calculating the speed of a sprinting athlete or the path of a stone thrown into a lake, the rules you learn here are the foundation for everything else in Physics. Don't worry if it seems a bit math-heavy at first; once you see the patterns, it becomes much easier!
1. The Language of Motion
Before we can calculate anything, we need to know exactly what we are measuring. In Physics, some words have very specific meanings that are slightly different from how we use them in daily life.
Distance vs. Displacement
Distance is a scalar quantity. it is the total length of the path traveled, regardless of direction. If you walk 5 meters east and 5 meters west, your distance is 10 meters.
Displacement is a vector quantity. It is the straight-line distance from your starting point to your finishing point, including the direction. In the example above, your displacement would be 0 meters because you ended up exactly where you started!
Speed vs. Velocity
Speed is how fast you are moving (distance ÷ time). It's a scalar.
Velocity is speed in a specific direction (displacement ÷ time). It's a vector. If a car travels at 20 m s\(^{-1}\) around a circular track at a constant speed, its velocity is constantly changing because its direction is changing.
Acceleration
Acceleration is the rate of change of velocity. It tells us how much the velocity changes every second. It is also a vector.
\( \text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}} \)
Quick Review Box:
• Scalars: Distance, Speed (Magnitude only)
• Vectors: Displacement, Velocity, Acceleration (Magnitude + Direction)
• Units: Distance/Displacement (m), Speed/Velocity (m s\(^{-1}\)), Acceleration (m s\(^{-2}\))
2. Understanding Motion through Graphs
Graphs are like "pictures" of motion. They make it much easier to see what is happening to an object over time. There are two main types you need to master:
Displacement-Time Graphs (\(s-t\))
This graph shows where an object is at any moment.
• A straight diagonal line means a constant velocity.
• A horizontal line means the object is stationary (not moving).
• A curved line means the velocity is changing (the object is accelerating).
Key Rule: The gradient (slope) of a displacement-time graph equals the velocity.
Velocity-Time Graphs (\(v-t\))
This graph shows how fast an object is going.
• A straight diagonal line means constant acceleration.
• A horizontal line means constant velocity (zero acceleration).
• Key Rule 1: The gradient (slope) of a velocity-time graph equals the acceleration.
• Key Rule 2: The area under the line of a velocity-time graph equals the displacement.
Common Mistake to Avoid: Students often confuse the area under the graph with the gradient. Just remember: Gradient = "Rate of change" (Velocity or Acceleration). Area = "Accumulation" (Displacement).
Key Takeaway: If you are stuck on a graph question, ask yourself: "Do I need the slope or the area?"
3. The Equations of Constant Acceleration (SUVAT)
When an object moves in a straight line with constant (uniform) acceleration, we can use five special variables called the SUVAT variables:
s = Displacement
u = Initial velocity
v = Final velocity
a = Acceleration
t = Time
The Big Four Equations:
1. \( v = u + at \)
2. \( s = \frac{(u + v)}{2}t \)
3. \( s = ut + \frac{1}{2}at^2 \)
4. \( v^2 = u^2 + 2as \)
Step-by-Step: How to Solve SUVAT Problems
1. Write down "S, U, V, A, T" in a list.
2. Fill in the values you know from the question.
3. Identify the value you are looking for.
4. Choose the equation that has the four variables you are dealing with (the three you know + the one you want).
5. Rearrange and solve!
Memory Aid: "SUVAT" is your best friend, but only if acceleration is constant! If the acceleration changes, you cannot use these equations.
4. Falling Objects and Gravity
When an object falls near the Earth's surface and we ignore air resistance, it falls with a constant acceleration called the acceleration of free fall, denoted by the symbol g.
On Earth, \( g \approx 9.81 \, \text{m s}^{-2} \).
Determining 'g' Experimentally
You need to know how to measure this in a lab. A common method involves:
1. Using an electromagnet to hold a steel ball.
2. When the current is switched off, the ball falls and a timer starts.
3. The ball hits a trapdoor or passes through a light gate, which stops the timer.
4. By measuring the height (\(s\)) and the time (\(t\)), and knowing \(u = 0\), we can use \( s = ut + \frac{1}{2}at^2 \) (which simplifies to \( g = \frac{2s}{t^2} \)) to calculate \(g\).
Did you know? In a vacuum (where there is no air), a hammer and a feather will hit the ground at exactly the same time because they both experience the same acceleration of \( 9.81 \, \text{m s}^{-2} \)!
5. Projectile Motion
What happens if you throw a ball sideways? It moves horizontally and vertically at the same time. This is called projectile motion.
The Golden Rule of Projectiles: The horizontal motion and the vertical motion are completely independent of each other. They do not affect one another.
How to break it down:
Horizontal Motion:
• There is no horizontal force (ignoring air resistance).
• Therefore, acceleration is zero (\(a = 0\)).
• The horizontal velocity remains constant throughout the flight.
Vertical Motion:
• Gravity acts downwards.
• Therefore, there is a constant acceleration (\(a = 9.81 \, \text{m s}^{-2}\)).
• We use the SUVAT equations for the vertical part of the calculation.
Analogy: Imagine two balls. One is dropped vertically, and the other is fired horizontally at the same time. Even though one is moving sideways, they will both hit the ground at the exact same moment because their vertical "lives" are identical!
Key Takeaway: When solving projectile problems, always split your workspace into two columns: Horizontal and Vertical. The only variable they share is Time (t).
Summary Checklist
Before moving on to Dynamics, make sure you can:
• Explain the difference between scalars (distance/speed) and vectors (displacement/velocity).
• Calculate velocity from an \(s-t\) graph gradient.
• Calculate acceleration and displacement from a \(v-t\) graph.
• Memorize and apply the four SUVAT equations.
• Describe an experiment to find \(g\).
• Solve projectile problems by treating horizontal and vertical motion separately.