1D/2D Kinematics with Calculus – AP Physics C | ShowMeClass

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Kinematics with Calculus

AP Physics C · Unit 1: Kinematics

Learning Objectives

Derive x(t), v(t), a(t) using derivatives & integrals

Interpret area under v-t curve as displacement

Analyze non-constant acceleration scenarios

Apply calculus-based kinematics in 2D projectile motion

Calculus Relations

Graph Colors

x(t) — Position

v(t) — Velocity

a(t) — Acceleration

Particle trajectory

Key Insight

Derivative gives instantaneous rate of change:
slope of x-t → v, slope of v-t → a

Integral gives accumulated quantity:
area under a-t → Δv, area under v-t → Δx

CalculusKinematicsDerivativesAP Physics C

t =—

x =—

v =—

a =—

x(t)

v(t)

a(t)

All

Acceleration Model

x₀ (m) 0

v₀ (m/s) 5

a₀ / A (m/s²) -2

ω (rad/s) 2

Launch Angle (°) 45

Duration (s) 6

Speed 1×

Calculus Analysis

📝 Quick Quiz▼

1. If v(t) = 3t² + 2, then a(t) is:

3t² + 2 6t t³ + 2t 6t + 2

2. The displacement from t=0 to t=T equals the:

Slope of x-t graph Area under the v-t curve Derivative of a(t) Maximum of v(t)

3. For a(t) = −g (projectile), v(t) is:

−gt² v₀ − gt −g/t v₀ + g