📘 AP Physics C Mechanics — Unit 1 Notes

Scalars & Vectors

  • Scalar: A quantity with magnitude only.
    Examples: time, mass, speed, temperature, distance.

  • Vector: A quantity with magnitude and direction.
    Examples: displacement, velocity, acceleration, force.

Vector Notation

  • Written with arrows: v⃗, a⃗, d⃗

  • Components:

A⃗=⟨Ax,Ay⟩

  • Magnitude:

∣A⃗∣=Ax2+Ay2

Adding Vectors

  • Component-wise:

R⃗=⟨Ax+Bx,  Ay+By⟩

Subtracting Vectors

  • Same idea:

R⃗=⟨Ax−Bx,  Ay−By⟩

🏃‍♂ Displacement, Velocity, Acceleration

Displacement

  • Change in position.

  • Vector.

Δx=xf−xi

Average Velocity

vavg=ΔxΔt

Instantaneous Velocity

  • Slope of the position–time graph.

  • In calculus: v(t)=x′(t).

  • In Physics C Unit 1: think slope.

Average Acceleration

aavg=ΔvΔt

Instantaneous Acceleration

  • Slope of the velocity–time graph.

  • In calculus: a(t)=v′(t).

  • In Physics C Unit 1: think slope.

📈 Graph Interpretations (SUPER important for Physics C)

Position vs Time

  • Slope = velocity

  • Curvature = acceleration

  • Straight line → constant velocity

  • Curved line → changing velocity

Velocity vs Time

  • Slope = acceleration

  • Area under curve = displacement

  • Straight line → constant acceleration

Acceleration vs Time

  • Area under curve = change in velocity

🚀 Constant Acceleration Equations (no calculus needed yet)

These come from integrating, but you can use them now:

  1. v=v0+at

  2. x=x0+v0t+12at2

  3. v2=v02+2a(x−x0)