Welcome to the World of Movement!
Ever wondered why some sprinters seem to "explode" out of the blocks, or why a long-jumper’s flight path is so predictable? It all comes down to Linear Motion. This chapter is a key part of your "Applied Movement Analysis" studies. We are going to look at how we measure movement in a straight (or curved) line and the math behind it.
Don't worry if math isn't your favorite subject—we’ll break every formula down into simple steps that make sense on the sports field!
1. The Fundamentals: Distance and Displacement
Before we can calculate how fast an athlete is moving, we need to know how far they have gone. There are two ways to measure this, and they are easily confused!
Distance
Distance is the total length of the path an object travels. It doesn't care about direction; it just cares about every single meter covered. We call this a scalar quantity because it only has "size" (magnitude).
Example: If a basketball player runs from the baseline to the halfway line (14m) and then runs back to the start (14m), the total distance covered is 28 meters.
Displacement
Displacement is the shortest straight-line route from the starting point to the finishing point. It must include a direction (e.g., "North" or "towards the goal"). This is a vector quantity because it has both size and direction.
Example: In that same basketball drill, if the player starts and ends at the baseline, their displacement is 0 meters because they ended up exactly where they started!
Quick Review: Scalar vs. Vector
To help you remember:
- Scalar = Size only (e.g., Distance, Speed)
- Vector = Value (Size) + Via (Direction) (e.g., Displacement, Velocity, Acceleration)
Key Takeaway: Distance is the total "ground covered," while displacement is how far "out of place" an object is.
2. Speed and Velocity
Now that we know how far an athlete has moved, we need to know how quickly they did it.
Speed
Speed is a scalar quantity. It tells us the rate at which an object covers distance.
The formula for speed is:
\( Speed = \frac{distance}{time} \)
The unit of measurement is meters per second (m/s).
Velocity
Velocity is the vector version of speed. It is the rate at which an object changes its position (displacement).
The formula for velocity is:
\( Velocity = \frac{displacement}{time} \)
Example: A 100m sprinter runs in a straight line. Because they aren't changing direction, their speed and velocity values will be the same. However, a swimmer doing two lengths of a 50m pool might have a high speed, but their average velocity would be zero because their displacement is zero!
Don't forget! Always include the unit m/s in your exam answers to get full marks.
3. Acceleration
In sport, athletes rarely move at the exact same speed for the whole game. They speed up, slow down, and change direction. This is Acceleration.
Acceleration is the rate of change of velocity. It is a vector quantity. To calculate it, we look at the difference between the starting velocity and the finishing velocity.
The Acceleration Formula
\( Acceleration = \frac{(final\ velocity\ –\ initial\ velocity)}{time\ taken} \)
The unit for acceleration is \( m/s^2 \) (meters per second squared).
Step-by-Step Example:
1. A sprinter starts from stationary (Initial Velocity = 0 m/s).
2. After 2 seconds (Time = 2s), they are running at 10 m/s (Final Velocity = 10 m/s).
3. \( Acceleration = \frac{10 - 0}{2} \)
4. \( Acceleration = 5\ m/s^2 \)
Did you know? If an athlete is slowing down (e.g., a long jumper landing in the sand), this is still called acceleration in physics, but the number will be negative (e.g., \( -2\ m/s^2 \)). This is often called deceleration.
Key Takeaway: Acceleration tells us how quickly an athlete's "speed in a direction" is changing.
4. Interpreting Graphs of Motion
The exam will often ask you to "plot, label, or interpret" graphs. Being able to read these is like having a map of an athlete's performance.
Distance-Time Graphs
- The Slope (Gradient): Represents the Speed.
- Steep line: The athlete is moving fast.
- Flat horizontal line: The athlete has stopped (stationary).
- Curved line: The athlete is changing speed (accelerating/decelerating).
Velocity-Time Graphs
This is the most common graph in PE exams!
- The Slope (Gradient): Represents the Acceleration.
- Line going up: Positive acceleration (speeding up).
- Line going down: Negative acceleration (slowing down).
- Flat horizontal line: Constant velocity (moving at a steady speed—NOT stopped!).
- Area under the graph: This represents the total displacement covered.
Common Mistake to Avoid:
On a Distance-Time graph, a flat line means the athlete has stopped.
On a Velocity-Time graph, a flat line means the athlete is moving at a steady speed.
Always check the labels on the axes before you start answering!
Quick Review Box:
- Speed: \( d/t \) (Scalar)
- Velocity: \( s/t \) (Vector)
- Acceleration: \( \frac{v-u}{t} \) (Vector)
- Slope of Distance-Time: Speed
- Slope of Velocity-Time: Acceleration
Summary Checklist
Before you move on, make sure you can:
1. Explain the difference between Distance (scalar) and Displacement (vector).
2. Calculate Speed and Velocity using the correct units (m/s).
3. Calculate Acceleration using the formula and correct units (\( m/s^2 \)).
4. Look at a graph and describe if an athlete is speeding up, slowing down, or moving at a constant pace.