Welcome to Unit 1: Kinematics!
Welcome to the start of your AP Physics 1 journey! Kinematics is the study of how things move. Before we look at why things move (forces), we need to master the language used to describe motion. Don't worry if this seems a bit math-heavy at first; once you see the patterns in the graphs and equations, it will start to click. We are going to look at objects moving in straight lines, speeding up, slowing down, and even falling through the air!
1.1 Scalars vs. Vectors: Direction Matters!
In physics, we categorize measurements into two groups. Understanding the difference is the first "secret" to getting problems right.
Scalars: These are simple. They only have a magnitude (a size or a number). Examples: Time (5 seconds), Mass (10 kg), or Temperature (20°C). Direction doesn't make sense here—you wouldn't say "5 seconds North!"
Vectors: These have both magnitude AND direction. Direction is everything in physics. Examples: Velocity (5 m/s East) or Displacement (10 meters up). We usually represent vectors with arrows.
Quick Tip: In AP Physics 1, we often use positive (+) and negative (-) signs to show direction. Usually, right/up is positive and left/down is negative.
1.2 Position, Distance, and Displacement
Imagine you are standing at a tree (your reference point). You walk 10 meters to the right, then 4 meters back to the left.
Distance (d): This is a scalar. It is the total ground you covered. In our example, you walked \(10 + 4 = 14\) meters. Distance is always positive.
Displacement (\(\Delta x\)): This is a vector. It is the straight-line change in position from where you started to where you ended. In our example, you ended up 6 meters to the right of the tree. So, your displacement is \(+6\) meters.
Formula: \(\Delta x = x_f - x_i\) (Final position minus Initial position).
Analogy: Your car's odometer measures distance. A GPS "as the crow flies" measurement from start to finish is displacement.
Key Takeaway: Distance is the "odometer" reading; displacement is the "shortcut" path from start to finish.
1.3 Speed and Velocity
People use these interchangeably in real life, but in physics, they are different!
Average Speed: A scalar. It is the total distance divided by time. \( \text{Speed} = \frac{\text{distance}}{\text{time}} \)
Average Velocity (\(v_{avg}\)): A vector. It is the displacement divided by time. \( v_{avg} = \frac{\Delta x}{\Delta t} \)
Instantaneous Velocity: This is your velocity at one specific moment in time. Think of looking down at your speedometer while driving.
Did you know? If you run exactly one lap around a circular track, your average velocity is zero because your displacement is zero! However, your average speed would be quite high.
1.4 Acceleration: Changing Motion
Acceleration (a) is the rate at which velocity changes. If you speed up, slow down, or change direction, you are accelerating!
Formula: \( a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t} \)
Common Mistake: Students often think negative acceleration always means "slowing down." That’s not true!
• If velocity and acceleration have the same sign (both + or both -), the object is speeding up.
• If they have opposite signs (+ velocity and - acceleration), the object is slowing down.
Key Takeaway: Acceleration tells you how many meters per second your velocity changes every second. That's why the unit is \( \text{m/s}^2 \).
1.5 The "Big 4" Kinematic Equations
When an object has constant acceleration, we can use these four power-house equations to solve almost any problem. You don't need to memorize them (they are on the AP formula sheet), but you must know when to use them!
1. \( v_f = v_i + at \) (Use this if you don't need displacement \(\Delta x\))
2. \( \Delta x = v_i t + \frac{1}{2}at^2 \) (Use this if you don't need final velocity \(v_f\))
3. \( v_f^2 = v_i^2 + 2a\Delta x \) (Use this if you don't need time \(t\))
4. \( \Delta x = \frac{1}{2}(v_i + v_f)t \) (Use this if you don't need acceleration \(a\))
Step-by-Step Problem Solving:
1. Draw a simple picture.
2. List your "knowns" (e.g., \(v_i = 0\), \(a = 2\), \(t = 5\)).
3. Identify what you are looking for (e.g., \(\Delta x = ?\)).
4. Pick the equation that has your "knowns" and your "unknown."
1.6 Representing Motion: Graphing
Graphs are the most common way AP Physics 1 tests your understanding of Kinematics. There are three main types:
1. Position vs. Time (\(x\) vs. \(t\))
• The slope of this graph equals the velocity.
• A straight diagonal line means constant velocity.
• A curved line means the object is accelerating (changing velocity).
2. Velocity vs. Time (\(v\) vs. \(t\))
• The slope equals the acceleration.
• The area under the curve (between the line and the zero-axis) equals the displacement (\(\Delta x\)).
• If the line is on the zero-axis, the object is stopped.
3. Acceleration vs. Time (\(a\) vs. \(t\))
• The area under the curve equals the change in velocity (\(\Delta v\)).
• In AP Physics 1, this graph is usually just horizontal lines because we mostly study constant acceleration.
Memory Aid: "Slope down, Area up."
Going from Position \(\rightarrow\) Velocity \(\rightarrow\) Acceleration? Use the Slope.
Going from Acceleration \(\rightarrow\) Velocity \(\rightarrow\) Position? Use the Area.
1.7 Free Fall: Gravity in Action
When an object is only moving under the influence of gravity (no air resistance), it is in free fall.
The Golden Rule: On Earth, all objects in free fall accelerate downward at \( g = 9.8 \, \text{m/s}^2 \) (On the AP exam, you can often use \( 10 \, \text{m/s}^2 \) to make the math easier!).
Important Facts for Problems:
• If you drop an object, its initial velocity \(v_i = 0\).
• If you throw an object up, at its highest point, its instantaneous velocity is 0.
• Even at the highest point, the acceleration is still \( -9.8 \, \text{m/s}^2 \). Gravity never "turns off" just because the object stopped moving for a split second!
Key Takeaway: In free fall problems, "a" is always a "freebie" piece of information: it's always \(-9.8 \, \text{m/s}^2\).
Quick Review Box
• Displacement: Final minus initial position (\(\Delta x\)).
• Velocity: Rate of change of position (slope of x-t graph).
• Acceleration: Rate of change of velocity (slope of v-t graph).
• Free Fall: Objects accelerate down at \(10 \, \text{m/s}^2\) regardless of mass.
• Speeding up: Velocity and acceleration have the same sign.
• Slowing down: Velocity and acceleration have opposite signs.