Welcome to Kinematics!

Have you ever wondered how your phone’s GPS calculates exactly when you'll arrive at your destination? Or how engineers design safe braking distances for cars? This is what Kinematics is all about!

In this chapter, we are going to study motion—specifically, how things move in a straight line. We won't worry about why they are moving (we’ll save forces for the next chapter); we just want to describe the "how." Don't worry if Physics has felt like a "maths-heavy" subject before—we will break it down step-by-step using simple logic and real-life stories.

1. The Language of Motion

Before we can solve problems, we need to speak the same language. There are six key terms you need to know. Don't worry if these seem similar at first; the difference is usually just about direction!

Distance vs. Displacement

  • Distance: The total ground covered. If you walk 5m forward and 5m back, your distance is 10m. (It's a scalar—it doesn't care about direction).
  • Displacement: Your change in position from the start point. In the example above, your displacement is 0m because you ended up exactly where you started! (It's a vector—direction matters).

Speed vs. Velocity

  • Speed: How fast you are moving (e.g., 50 km/h).
  • Velocity: Speed in a specific direction (e.g., 50 km/h North).

Acceleration

Acceleration is the rate of change of velocity. If you speed up, slow down, or even just change direction, you are accelerating!

Quick Tip: The Sign Matters!

In Kinematics, we usually use (+) for one direction (like Right or Up) and (-) for the opposite direction (like Left or Down). If an object is slowing down, its acceleration usually has the opposite sign to its velocity.

Key Takeaway: Displacement, Velocity, and Acceleration are vectors. Always ask yourself: "Which way is it moving?"

2. Seeing Motion: Graphs

Sometimes a picture is worth a thousand equations. We use two main types of graphs in H1 Physics:

Displacement-Time (\(s-t\)) Graphs

  • The Gradient (slope) represents the Velocity.
  • A flat horizontal line means the object is stationary (velocity = 0).
  • A straight diagonal line means constant velocity.
  • A curve means the velocity is changing (the object is accelerating).

Velocity-Time (\(v-t\)) Graphs

  • The Gradient represents the Acceleration.
  • The Area under the graph represents the Displacement.
  • A horizontal line here means constant velocity (acceleration = 0).
Did you know?

Even if an acceleration is "non-uniform" (changing), the rules for gradients and areas still apply! You might need to draw a tangent to a curve to find the gradient at a specific point.

Key Takeaway: Use the "G-A Rule" for \(v-t\) graphs: Gradient = Acceleration; Area = Displacement.

3. The Equations of Motion (SUVAT)

When an object moves with constant (uniform) acceleration in a straight line, we can use five variables, often called SUVAT:

\(s\) = displacement
\(u\) = initial velocity
\(v\) = final velocity
\(a\) = acceleration
\(t\) = time

The Big Four Equations

You need to be able to use these to solve problems:

1. \( v = u + at \)
2. \( s = \frac{1}{2}(u + v)t \)
3. \( s = ut + \frac{1}{2}at^2 \)
4. \( v^2 = u^2 + 2as \)

How to Derive Them (The Simple Way)

You might be asked where these come from. It's easier than it looks!

Equation 1 comes from the definition of acceleration: \( a = \frac{v - u}{t} \). Just multiply by \(t\) and move the \(u\) over!

Equation 2 comes from the area of a trapezoid under a \(v-t\) graph (Average Velocity \(\times\) Time).

Common Mistake to Avoid:

Never use these equations if the acceleration is changing! They only work for uniform acceleration. If acceleration changes, go back to using graphs.

Key Takeaway: When solving a problem, list your "SUVAT" variables first to see which ones you have and which one you need to find!

4. Free Fall: Motion Under Gravity

In H1 Physics, when we talk about an object falling "without air resistance," it is in Free Fall.

  • The acceleration is always constant: \( a = 9.81 \, \text{m s}^{-2} \).
  • This acceleration acts downwards toward the center of the Earth.
  • Whether you drop a heavy bowling ball or a small marble, they both accelerate at the same rate!
Step-by-Step for Free Fall Problems:

1. Pick a direction to be positive. (Usually "Up" is positive).
2. Set your acceleration. If "Up" is positive, then \( a = -9.81 \, \text{m s}^{-2} \).
3. Identify your 'u'. If an object is "dropped," \( u = 0 \). If it's "thrown up," \( u \) is positive.
4. At the highest point of a throw, the velocity \( v \) is always 0 for a split second.

Key Takeaway: Gravity is just a specific type of constant acceleration (\(g\)). Use the SUVAT equations just like before!

5. Quick Review & Summary

Mastered the basics? Check these off:

  • I can explain the difference between Distance (total path) and Displacement (start to end).
  • I know that Velocity is the gradient of a displacement-time graph.
  • I know that Acceleration is the gradient of a velocity-time graph.
  • I know that Displacement is the area under a velocity-time graph.
  • I can list the 4 SUVAT equations and use them for constant acceleration.
  • I remember that for free fall, \( a = 9.81 \, \text{m s}^{-2} \) downwards.

Don't worry if this feels like a lot to memorize. The more you practice "listing your SUVAT variables" for every problem, the more natural it will become. You've got this!