Speed, Velocity, Acceleration, and Free Fall Study Guide (copy)

Speed

A scalar physical quantity that represents how fast an object moves regardless of direction.

Galileo Galilei

The first scientist to quantitatively define speed by measuring distance traveled divided by elapsed time.

SI Unit of Speed

Meters per second (m/s or m s^{-1}).

Instantaneous Speed

The speed of an object at any precise instant in time.

Average Speed

Total distance traversed divided by the total time duration to cover that distance.

Displacement

The net change in position of an object, represented by the formula Δx = x_final - x_initial.

Average Velocity

The displacement divided by the total time interval.

Acceleration

The rate of change of velocity with respect to time, expressed as a vector quantity with both magnitude and direction.

Free Fall

An object in free fall moves exclusively under the influence of Earth's gravity, with negligible air resistance.

Velocity

The rate of change of displacement over time, a vector quantity that includes both magnitude and direction.

Units of Acceleration

SI unit is meters per second squared (m/s² or m s^{-2}).

Displacement vs. Distance Travelled

Displacement measures the straight-line distance and direction from start to end, while distance travelled is the cumulative length of path taken.

Average Speed Formula

Average speed = total distance travelled / total time interval.

Kinematics Equation: Velocity-Time Relation

v_f = v_i + a Δt.

Kinematics Equation: Position-Time Relation

Δx = v_i Δt + (1/2)a(Δt)^2.

Kinematics Equation: Velocity-Position Relation

v_f² = v_i² + 2aΔx.

Kinematics Equation: Displacement-Average Velocity Relation

Δx = (1/2)(v_i + v_f)Δt.

Free Fall Acceleration

Constantly directed downward toward Earth's center with a magnitude of approximately 9.8 m/s².

Object in Uniform Acceleration

Motion where acceleration remains constant in both magnitude and direction.

Speed vs. Velocity

Speed is a scalar indicating magnitude only, whereas velocity is a vector indicating both magnitude and direction.