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Physics Unit 1: Kinematics

Kinematics describes motion without asking what causes it. With constant acceleration, four equations handle almost every problem.

Covers: Position, displacement, velocity, acceleration, motion graphs, constant-acceleration equations, free fall, projectiles

Study guide

Kinematics describes motion without asking what causes it. Position tells where an object is; displacement is the change in position, a vector with direction, while distance is the total path length. Velocity is the rate of change of position (displacement ÷ time), and speed is its magnitude. Acceleration is the rate of change of velocity, measured in m/s². An object slows down when its acceleration points opposite its velocity.

Motion graphs encode the same information. On a position-time graph, the slope is velocity, and a curved line means changing velocity. On a velocity-time graph, the slope is acceleration and the area under the curve is displacement. On an acceleration-time graph, the area is the change in velocity.

For constant acceleration, four equations connect the variables: v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx; and Δx = ½(v₀ + v)t. Pick the equation that contains your three known values and the unknown, and choose a positive direction to keep signs consistent.

In free fall, the only acceleration is gravity, g ≈ 9.8 m/s² downward, regardless of mass if air resistance is ignored. An object thrown upward slows down, momentarily stops at the top (v = 0, but a is still 9.8 m/s² downward), then speeds up coming down.

Projectile motion splits into independent horizontal and vertical parts. Horizontal velocity stays constant (no horizontal acceleration), while vertical motion is free fall. Break the launch velocity into components with v₀cos θ and v₀sin θ, use the vertical motion to find the time, and use that time for the horizontal distance. Launched at the same speed, 45° gives the greatest range on level ground.

A vector has both magnitude and direction. Examples are displacement, velocity, acceleration, force, momentum and electric field. A scalar has only magnitude, such as distance, speed, time, mass, energy and work. Average velocity is the slope of the straight line between two points on a position-time graph. Instantaneous velocity is the slope of the tangent line at a single point. A steeper tangent means a faster speed, and a horizontal tangent means the object is momentarily at rest.

Measured velocity depends on the observer's reference frame. A ball tossed straight up inside a moving train goes straight up and down for a passenger, but a person on the ground sees it follow a curved path. To find an object's velocity relative to the ground, add its velocity relative to the moving frame to the frame's own velocity, as vectors.

Key ideas

• Displacement is change in position (a vector); distance is total path length.
• Velocity is the slope of a position-time graph; acceleration is the slope of a velocity-time graph.
• Area under a velocity-time graph is displacement.
• In free fall, a = g ≈ 9.8 m/s² downward (ignoring air resistance).
• Projectiles: horizontal velocity is constant; vertical motion is free fall.

Formulas and rules

Common mistakes

• Using distance when the question asks for displacement.
• Giving a horizontally launched projectile a horizontal acceleration.

Words to know

Velocity (from a graph)

The slope of a position–time graph.

Displacement (from a graph)

The area under a velocity–time graph.

Free-fall acceleration (g)

About 9.8 m/s², downward.

Velocity–time equation

v = v₀ + at, for constant acceleration.

Projectile horizontal velocity

Constant, with no air resistance.

Displacement

Change in position, a vector.

Distance

The total path length, a scalar.

Velocity

Displacement ÷ time, with direction.

Acceleration

The rate of change of velocity (m/s²).

Δx = v₀t + ½at²

Displacement with constant acceleration.

v² = v₀² + 2aΔx

The kinematics equation without time.

Projectile motion

Constant horizontal velocity plus vertical free fall.

Velocity components

v₀ₓ = v₀cos θ, v₀ᵧ = v₀sin θ

Velocity at the top of a throw

Zero (vertical), while acceleration is still g downward.

Sample practice questions

23 more questions like these, from level 1 to 5, are in the practice set.