Crash Course — Unit 1: Kinematics

• Scalar vs. Vector
  €” Scalars have magnitude only (like speed, 55 mph). Vectors have magnitude AND direction (like velocity, 55 mph North).
• Position (x)
  €” Your location on an axis or coordinate system.
• Distance (d)
  €” The total path you've traveled, like the reading on a car's odometer. It's a scalar.
• Displacement (Δx)
  €” Your straight-line change in position from start to finish. It's a vector.
• Speed (v)
  €” How fast you're going; the rate of change of distance. It's a scalar.
• Velocity (v)
  €” How fast you're going and in what direction; the rate of change of position. It's a vector.
• Acceleration (a)
  €” The rate of change of velocity. You can accelerate by speeding up, slowing down, or just changing direction.
• Motion Graphs
  €” The "Big Three" graphs (position, velocity, acceleration vs. time) are visual stories of motion. The slope and area of these graphs have physical meanings.
• Slope & Area Rules
  €” The slope of a position-time graph is velocity. The slope of a velocity-time graph is acceleration. The area under a velocity-time graph is displacement.
• Reference Frames
  €” All motion is relative. A person walking on a train has a different velocity relative to the train than they do relative to the ground.
• Vector Components
  €” Any vector at an angle can be broken down into two perpendicular parts (x and y) that are easier to work with.
• Independence of Motion
  €” In 2D problems (like a thrown baseball), the horizontal motion and vertical motion are completely separate. They only share time.

Key Formulas / Terms

• Average Velocity: v_avg = Δx / Δt (Your displacement over a time interval)
• Average Acceleration: a_avg = Δv / Δt (The change in your velocity over a time interval)
• The Kinematic Equations (for CONSTANT acceleration only!):
  • v = v₀ + at (The "no displacement" equation)
  • x = x₀ + v₀t + ½at² (The "go-to" equation for finding position)
  • v² = v₀² + 2a(x - x₀) (The "no time" equation)
• Vector Components (for a vector V at angle θ from the horizontal):
  • Horizontal component: V_x = V cos(θ)
  • Vertical component: V_y = V sin(θ)

Exam Traps

• Trap
  Confusing scalars and vectors. The exam will give you a story problem about a runner on a track and ask for their displacement, hoping you calculate the total distance they ran. · Counter: Before you calculate, highlight the word in the question: "displacement" means start-to-finish vector, "distance" means total path scalar. "Velocity" needs a direction, "speed" does not.
• Trap
  Assuming negative acceleration always means "slowing down." They'll describe an object moving in the negative direction and speeding up (like a ball rolling down a ramp to the left). · Counter: Say this out loud: "Slowing down happens when velocity and acceleration have opposite signs. Speeding up happens when they have the same sign." Direction matters!
• Trap
  Misinterpreting motion graphs. You'll see a horizontal line on a velocity-time graph and your brain will scream "it's stopped!" · Counter: The instant you see a graph, circle the label on the y-axis. A horizontal line on a v-t graph means constant velocity, not zero position. An object moving at a steady 5 m/s is not stopped.
• Trap
  Using the kinematic equations when acceleration is not constant. A problem might show a curved velocity-time graph and tempt you to plug values into your favorite formula. · Counter: The kinematic equations are your reward for proving acceleration is constant. If it's not, you must use the graph itself. Find the slope for acceleration or the area for displacement.
• Trap
  Forgetting that 2D motion is just two 1D problems. For a projectile, you might be tempted to use the initial launch speed in a vertical motion calculation. · Counter: Make a T-chart. Immediately separate all information into an "X" column and a "Y" column. The only variable they share is time (t). Gravity (a = -9.8 m/s²) ONLY goes in the Y-column.