Welcome to Kinematics!
Welcome to the first part of your journey into Motion. Kinematics is essentially the "math of moving." We aren't worried about why things move yet (that's where forces come in later); we just want to describe how they move. Whether it’s a sprinter on a track, a car braking, or a ball flying through the air, the rules you’ll learn here apply to them all.
Don't worry if some of the graphs or equations look a bit daunting at first—we’re going to break them down step-by-step until you’re a pro!
1. The Language of Motion
Before we can calculate anything, we need to speak the same language. In Physics, we use very specific terms that might mean something slightly different in everyday life.
Distance vs. Displacement
• Distance is a scalar. It’s just "how much ground you’ve covered." If you run 100m and then turn around and run 100m back, your distance is 200m.
• Displacement is a vector. It’s "how far out of place you are" from where you started. In that same run, your displacement is 0m because you ended up exactly where you began!
Speed vs. Velocity
• Average Speed is the total distance divided by the total time. \( \text{speed} = \frac{\text{distance}}{\text{time}} \).
• Velocity is speed in a specific direction. It is the rate of change of displacement. \( v = \frac{\Delta s}{\Delta t} \).
• Instantaneous Speed is your speed at one specific moment (like looking at a car's speedometer).
Acceleration
Acceleration is the rate of change of velocity. If you are speeding up, slowing down, or even just turning a corner at a constant speed, you are accelerating because your velocity is changing.
\( \text{Acceleration} (a) = \frac{\Delta v}{\Delta t} \)
Quick Review:
1. Scalars (Distance, Speed) only have a size.
2. Vectors (Displacement, Velocity, Acceleration) have a size AND a direction.
2. Seeing Motion: Graphs
Graphs are like a "movie" of an object's movement frozen on paper. There are two main types you need to master.
Displacement–Time Graphs (s-t)
Imagine you are hiking up a hill. The steeper the hill, the faster you are climbing.
• The gradient (slope) of an s-t graph tells you the velocity.
• A straight diagonal line means constant velocity.
• A flat horizontal line means the object is stationary (velocity is zero).
• A curve means the object is accelerating.
Velocity–Time Graphs (v-t)
This is where students often get confused, so here is a simple trick:
• The gradient tells you the acceleration.
• The area under the graph tells you the displacement (how far it traveled).
Example: If you have a rectangle on a v-t graph with a height of \( 10 \, \text{m s}^{-1} \) and a width of \( 5 \, \text{s} \), the area is \( 10 \times 5 = 50 \, \text{m} \). That’s how far the object moved!
Did you know? If you have a curved v-t graph, you can estimate the area by counting the squares underneath it. This is a common exam task!
Key Takeaway: s-t gradient = velocity. v-t gradient = acceleration. v-t area = displacement.
3. The "SUVAT" Equations (Linear Motion)
When an object is moving with constant acceleration in a straight line, we use the "Fantastic Four" equations. We call them SUVAT because of the five variables involved:
• \( s \) = displacement (m)
• \( u \) = initial velocity (\( \text{m s}^{-1} \))
• \( v \) = final velocity (\( \text{m s}^{-1} \))
• \( a \) = acceleration (\( \text{m s}^{-2} \))
• \( t \) = time (s)
The Equations:
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 Solve SUVAT Problems:
Step 1: Write down "S, U, V, A, T" in a list.
Step 2: Fill in the values you know from the question.
Step 3: Identify which value you are trying to find.
Step 4: Pick the equation that has the four variables you are working with (the three you know + the one you want).
Common Mistake to Avoid: Always check your signs! If you decide that "up" is positive, then any downward acceleration (like gravity) must be negative (\( -9.81 \)).
4. Free Fall and Gravity
When you drop an object, gravity pulls it down. If we ignore air resistance, all objects fall with the same acceleration regardless of their mass. This is called the acceleration of free fall, denoted by \( g \).
• On Earth, \( g = 9.81 \, \text{m s}^{-2} \).
• When an object is thrown upwards, it slows down at a rate of \( 9.81 \, \text{m s}^{-2} \) until it hits a velocity of zero at its highest point, then it starts falling back down, speeding up at the same rate.
Key Takeaway: In any "drop" or "throw" problem, you always know \( a = 9.81 \) (or \( -9.81 \)). It's a "hidden" number you get for free!
5. Real-World Motion: Stopping Distances
In the real world, a car doesn't stop instantly. The Total Stopping Distance is made up of two parts:
1. Thinking Distance: The distance traveled from the moment you see a hazard until you hit the brakes. This is affected by your reaction time (tiredness, alcohol, or distractions).
2. Braking Distance: The distance traveled while the brakes are being applied. This is affected by the car's speed, the road conditions (ice/rain), and the condition of the tires/brakes.
\( \text{Stopping Distance} = \text{Thinking Distance} + \text{Braking Distance} \)
6. Projectile Motion
What happens if you throw a ball sideways? It moves horizontally and vertically at the same time. This is Projectile Motion.
The most important rule in Projectiles is: The horizontal and vertical motions are completely independent!
The Split Strategy:
To solve these, split your page into two columns:
Horizontal Motion:
• There is no acceleration (if we ignore air resistance).
• The velocity stays constant the whole time.
• Use: \( \text{distance} = \text{velocity} \times \text{time} \).
Vertical Motion:
• There is constant acceleration (\( g = 9.81 \, \text{m s}^{-2} \)).
• The object speeds up as it falls.
• Use: SUVAT equations.
Memory Aid: The only thing that is the same for both columns is Time (\( t \)). Time is the bridge that connects horizontal and vertical motion.
Quick Summary:
• Kinematics describes motion using vectors and scalars.
• Graphs help us visualize change (gradient and area).
• SUVAT is for constant acceleration in a line.
• Projectiles require splitting the problem into horizontal (constant speed) and vertical (gravity) parts.