Motion

The One Thing

Motion is a change in an object’s position with time relative to a chosen reference point. Distance, displacement, speed, velocity and acceleration describe different aspects of this change, while the equations of motion apply to uniformly accelerated motion.

Reactions, Processes and Experiments

Key Terms

• Motion: A body is in motion if its position changes with time relative to a chosen reference point.
• Rest: A body is at rest if its position does not change with time relative to a chosen reference point.
• Reference point: A fixed point or object used to decide whether another object is moving or at rest.
• Distance: The total length of the actual path travelled by an object. It is a scalar quantity and is always zero or positive.
• Displacement: The shortest straight-line distance from the initial position to the final position, together with direction. It is a vector quantity.
• Scalar quantity: A physical quantity described by magnitude only, such as distance, speed and time.
• Vector quantity: A physical quantity described by both magnitude and direction, such as displacement, velocity and acceleration.
• Speed: The distance travelled per unit time. Average speed equals total distance divided by total time.
• Velocity: The displacement per unit time in a specified direction. Average velocity equals displacement divided by time.
• Uniform motion: Motion in which an object covers equal distances in equal intervals of time.
• Non-uniform motion: Motion in which an object covers unequal distances in equal intervals of time, or changes direction.
• Acceleration: The rate of change of velocity with time. It may be positive, negative or zero.
• Retardation: Negative acceleration, in which the velocity decreases with time.
• Uniform acceleration: Acceleration in which velocity changes by equal amounts in equal intervals of time.
• Position-time graph: A graph showing how an object’s position changes with time. Its slope represents velocity.
• Velocity-time graph: A graph showing how velocity changes with time. Its slope represents acceleration, and the area under the graph represents displacement.
• Uniform circular motion: Motion along a circular path with constant speed. Its velocity changes continuously because its direction changes.
• Initial velocity, $u$: The velocity of an object at the beginning of the time interval.
• Final velocity, $v$: The velocity of an object at the end of the time interval.
• Acceleration, $a$: The change in velocity per unit time.
• Time, $t$: The duration for which motion is considered.
• Displacement, $s$: The change in position, measured as a directed straight-line distance.

Relevant SI units are metre (m) for distance and displacement, second (s) for time, metre per second (m/s) for speed and velocity, and metre per second squared (m/s²) for acceleration.

Easily Confused

• Distance and displacement: Distance is the total actual path and is scalar; displacement is the shortest straight-line change from initial to final position and includes direction.
• Speed and velocity: Speed is distance per unit time without direction; velocity is displacement per unit time in a specified direction.
• Motion and rest: Both depend on the chosen reference point; the same object may be at rest relative to one object and in motion relative to another.
• Uniform and non-uniform motion: Uniform motion covers equal distances in equal time intervals; non-uniform motion covers unequal distances or involves a change of direction.
• Speed and velocity in uniform circular motion: Speed may remain constant, but velocity changes continuously because direction changes.
• Distance and displacement on returning to the starting point: Displacement is zero, but distance travelled is not zero.
• Acceleration and retardation: Acceleration is the rate of change of velocity; retardation is negative acceleration in which velocity decreases.
• Position-time and velocity-time graphs: The slope of a position-time graph gives velocity, whereas the slope of a velocity-time graph gives acceleration; the area under a velocity-time graph gives displacement.
• Constant velocity and uniform acceleration: Constant velocity has zero acceleration; uniform acceleration involves equal changes in velocity in equal time intervals.
• One-dimensional and two-dimensional motion: A car moving on a straight road is one-dimensional, whereas a stone thrown at an angle is two-dimensional.

What Gets Asked

• Definitions and distinctions: Questions may ask for motion, rest, reference point, distance, displacement, speed, velocity, acceleration or retardation. Marks are lost by omitting direction from displacement or velocity.
• Numerical calculations: Questions may require average speed, average velocity or acceleration. The relevant distinction is total distance for average speed and total displacement for average velocity.
• Equations of motion: Problems may require use of $v=u+at$, $s=ut+1/2a{t}^2$, $v^2=u^2+2as$, or $s=(u+v)t÷2$. These equations apply only when acceleration is uniform.
• Special cases: For an object starting from rest, use $u=0$, giving $v=at$ and $s=1/2a{t}^2$. For constant velocity, acceleration is zero and $s=vt$.
• Graph interpretation: Questions may ask for the slope of a position-time or velocity-time graph, or the area under a velocity-time graph. The common error is confusing velocity with acceleration or failing to interpret area as displacement.
• Path and direction: Problems may involve an object returning to its starting point or moving in uniform circular motion. The key issue is that distance can be non-zero when displacement is zero, and constant speed does not necessarily mean constant velocity.