Kinematics Formulas to Know for AP Physics 1 (AP)

Kinematics equations

They describe the relationships between velocity, acceleration, and displacement, providing the tools to solve a wide range of motion-related physics problems.

v = v₀ + at

Relates final velocity (v) to initial velocity (v₀), acceleration (a), and time (t).

v = v₀ + at

Used for scenarios with uniform acceleration.

Δx = v₀t + ½at²

Calculates displacement (Δx) under constant acceleration.

Δx = v₀t + ½at²

Combines the effects of initial velocity and acceleration over time. Useful for determining distance traveled from rest or with an initial velocity.

v² = v₀² + 2aΔx

Links the squares of velocities to acceleration and displacement.

v² = v₀² + 2aΔx

Helpful when time is unknown or unnecessary. Highlights the connection between kinetic energy and work.

x = x₀ + vt (for constant velocity)

Describes position (x) of an object moving at a constant velocity (v). Shows displacement as directly proportional to time for constant velocity.

v_avg = (v + v₀) / 2

Calculates average velocity (v_avg) for uniformly accelerating objects. Represents the arithmetic mean of initial and final velocities.

v_avg = Δx / Δt

Defines average velocity as total displacement (Δx) divided by total time (Δt).

a = Δv / Δt

Defines acceleration (a) as the rate of change in velocity (Δv) over time (Δt). Indicates how quickly an object accelerates or decelerates.

Δx = v_avg * t

Calculates displacement (Δx) using average velocity (v_avg) and time (t). Works for both constant and variable velocities.

x = ½(v + v₀)t

Computes displacement (x) from the average of initial and final velocities over time.

x = ½(v + v₀)t

Derived from average velocity, suitable for uniformly accelerated motion.

Δy = v₀y * t + ½gt²

for vertical motion under gravity

Δy = v₀y * t + ½gt² (for vertical motion under gravity)

Describes vertical displacement (Δy) under gravity’s influence. Includes initial vertical velocity (v₀y) and gravitational acceleration (g).

Δy = v₀y * t + ½gt²

Crucial for solving projectile motion and free-fall problems.

Δx = v_avg * t

Simplifies distance calculations over a time period.

x = ½(v + v₀)t

Helps determine distance when acceleration is involved.

x = x₀ + vt (for constant velocity)

Used to find an object’s position without acceleration.