Movement and position

Movement and position are described using the quantities distance, displacement, speed, velocity, and acceleration.

Distance and speed are scalars, while displacement, velocity, and acceleration are vectors (they have both magnitude and direction).

Key Definition Speed is the distance travelled per unit time and is a scalar, while velocity is speed in a stated direction and is a vector.

Key Definition Acceleration is the change in velocity per unit time, and it too is a vector — a negative value indicates deceleration.

Equations of Motion

Average speed is calculated from the distance travelled and the time taken using:

v = d / t

Acceleration connects the change in velocity to the time interval over which that change occurs:

a = (v − u) / t

When the time is unknown, the following equation links the final speed, initial speed, acceleration, and distance moved:

v² = u² + 2as

Motion Graphs

Motion graphs are powerful tools for analysing movement.

Distance–Time Graph

• The gradient represents the speed of the object
• A steeper line means the object is moving faster
• A horizontal line means the object is stationary
• A curve means the speed is changing (the object is accelerating or decelerating)

Velocity–Time Graph

• The gradient represents the acceleration of the object
• A horizontal line means constant velocity (zero acceleration)
• The area between the line and the time axis represents the distance travelled
• Complex areas can be broken into rectangles, triangles, and trapeziums and calculated separately

Practical Investigations

Practical investigations of motion require careful control of variables, repeated measurements, and an understanding that reaction time introduces random error.

Unit conversions — particularly km/h to m/s — must be performed before substituting values into any equation.