Kinematics: every key term you need (+ practice quiz)

More AP Physics 1 guides

• Forces and Newton's Laws
• Work, Energy and Power
• Momentum and Collisions
• Circular Motion and Gravitation
• Simple Harmonic Motion

Kinematics Definition

Study of motion without regard to forces; describes position, velocity, acceleration using equations and graphs.

Displacement vs Distance

Displacement: change in position, vector (has direction). Distance: total path length, scalar. Same magnitude if straight path.

Velocity vs Speed

Velocity: displacement/time, vector. Speed: distance/time, scalar. Average velocity = Δx/Δt; instantaneous velocity = limit of average.

Acceleration

Rate of change of velocity; vector quantity. a = Δv/Δt. Positive = speeding up in positive direction or slowing down in negative direction.

Constant Acceleration

Acceleration doesn't change over time; enables use of kinematic equations: v=v₀+at, x=v₀t+½at², v²=v₀²+2aΔx.

Kinematic Equations (4 total)

v=v₀+at, x=v₀t+½at², v²=v₀²+2ax, x=½(v₀+v)t. Choose based on which variable is missing.

Position-Time Graphs

Slope = velocity. Straight line = constant velocity. Curved line = acceleration. Steeper = faster. Downward = negative velocity.

Velocity-Time Graphs

Slope = acceleration. Area under curve = displacement. Horizontal line = constant velocity (zero acceleration).

Acceleration-Time Graphs

Area under curve = change in velocity. Horizontal line = constant acceleration. Above x-axis = speeding up (same direction as v).

Free Fall

Motion under gravity alone; acceleration = -9.8 m/s² (downward). v increases downward, displacement increases each second.

Projectile Motion

Two-dimensional motion with constant horizontal velocity and vertical acceleration due to gravity.

Horizontal & Vertical Components

Analyze separately: x-direction (no acceleration, constant velocity); y-direction (constant acceleration = g).

Projectile Range

Horizontal distance traveled. Formula: R = v₀²sin(2θ)/g. Maximum range at 45° launch angle.

Relative Velocity

Velocity of object A relative to object B = velocity of A - velocity of B. Add velocities as vectors.

Unit 1 Summary

Kinematics equations describe motion; displacement, velocity, acceleration are vectors. Constant acceleration enables algebraic solutions. Projectile motion combines constant horizontal velocity with vertical acceleration.

Instantaneous vs Average Acceleration

Instantaneous acceleration is the slope of the tangent to a v-t graph at one instant; average acceleration is the slope of the secant between two points. They agree only when acceleration is constant.

Sign of Acceleration and Speeding Up

An object speeds up when velocity and acceleration have the same sign and slows down when they differ. Negative acceleration does not mean slowing down.

Curvature of x-t Graphs

A position-time graph that is concave up has positive acceleration; concave down has negative acceleration. An inflection point marks where acceleration changes sign.

Odd-Number Rule for Free Fall

From rest, distances fallen in successive equal time intervals are in the ratio 1:3:5:7, because total distance grows as t^2 (1, 4, 9, 16).

Symmetry of Projectile Flight

Over level ground, time up equals time down, launch speed equals landing speed, and the angle below horizontal at landing equals the launch angle above.

Complementary Launch Angles

Angles θ and 90° − θ give the same range on level ground because sin(2θ) = sin(180° − 2θ), but the higher angle has a longer flight time and greater max height.

Maximum Height of a Projectile

H = (v₀ sinθ)^2 / (2g). Only the vertical component matters, so doubling launch speed quadruples the maximum height.

Time of Flight

For a level-ground projectile, T = 2v₀ sinθ / g. Time depends only on the vertical component; horizontal speed has no effect on how long it stays airborne.

Vector Decomposition

Any vector at angle θ from the x-axis has components A cosθ (x) and A sinθ (y). Choose axes to simplify the problem, e.g. along an incline.

Relative Motion in Two Dimensions

A boat aimed across a river drifts downstream because velocities add as vectors: v_boat/ground = v_boat/water + v_water/ground. Crossing time depends only on the component perpendicular to the current.

Zero Velocity, Nonzero Acceleration

An object can be momentarily at rest while accelerating (ball at top of toss, mass at the end of a spring's swing). Velocity is zero for an instant; acceleration is not.

Meeting Problems

Two objects meet when their positions are equal at the same time. Write x(t) for each with a common origin and clock, then set them equal and solve for t.

Reaction-Time Stopping Distance

Total stopping distance = v·t_reaction + v^2/(2a). The first term is linear in speed, the braking term is quadratic, so doubling speed more than doubles stopping distance.

Graph Translations

Given a v-t graph, sketch a-t by reading slopes and x-t by accumulating area. Given x-t, velocity comes from slope; you cannot recover initial position from a v-t graph alone.

Terminal Velocity (qualitative)

With air resistance, a falling object's acceleration decreases as speed grows until drag balances weight; velocity approaches a constant terminal value, so the v-t graph flattens.