Motion in One Dimension

The One Thing

One-dimensional motion describes how an object’s position changes with time along a single straight line. It is analysed by distinguishing scalar quantities from vector quantities and by using equations and graphs to relate position, velocity, acceleration, and time.

Reactions, Processes and Experiments

Key Terms

• Rest: A state in which an object’s position does not change with respect to a chosen reference point.
• Motion: A change in an object’s position with respect to a chosen reference point over time.
• Reference point: A fixed object or location used to decide whether another object is at rest or in motion.
• Position: The location of an object relative to a reference point.
• 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 its 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; it indicates how fast an object moves but not its direction.
• Average speed: The total distance travelled divided by the total time taken.
• Velocity: The displacement covered per unit time in a specified direction.
• Average velocity: The total displacement divided by the total time taken.
• 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 its direction.
• Acceleration: The rate of change of velocity with time.
• Uniform acceleration: Acceleration in which velocity changes by equal amounts in equal intervals of time.
• Retardation or deceleration: Negative acceleration, in which velocity decreases with time.
• One-dimensional motion: Motion along a single straight line, represented using one coordinate or direction.
• Instantaneous speed: The speed of an object at a particular instant.
• Instantaneous velocity: The velocity of an object at a particular instant, including its direction.

Easily Confused

• Distance and displacement: Distance is the total actual path length 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 and has no direction; velocity is displacement per unit time and includes direction.
• Average speed and average velocity: Average speed uses total distance divided by total time; average velocity uses total displacement divided by total time.
• Uniform motion and uniform acceleration: Uniform motion involves equal distances in equal time intervals; uniform acceleration involves equal changes in velocity in equal time intervals.
• Zero velocity and zero acceleration: An object can have zero velocity at an instant but non-zero acceleration, as for a ball at the highest point of its upward motion.
• Distance and magnitude of displacement: Distance is always greater than or equal to the magnitude of displacement; they are equal only when an object moves in a straight line without changing direction.
• Returning to the starting point and travelling zero distance: Returning to the starting point makes displacement zero, but the distance travelled is not zero.
• Positive or negative velocity and speeding up or slowing down: A sign represents direction in one-dimensional motion; it does not automatically indicate whether the object is speeding up or slowing down.
• 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.

What Gets Asked

• Definitions and classifications: Questions may ask students to distinguish rest, motion, reference point, scalar quantities, vector quantities, uniform motion, non-uniform motion, acceleration, and one-dimensional motion. Marks are lost when direction is omitted from vector quantities.
• Distance and displacement calculations: Questions may provide a path or a return to the starting point. The common error is to set distance equal to displacement when the object changes direction or returns to its starting point.
• Speed and velocity calculations: Questions may require average speed or average velocity. The specific slip is using total distance for average velocity or total displacement for average speed.
• Unit conversions: Questions may require conversion between m/s and km/h using 1 m/s = 18/5 km/h and 1 km/h = 5/18 m/s. Marks are lost when units are not converted consistently.
• Equations of uniformly accelerated motion: Questions may require use of v = u + at, s = ut + 1/2 at², v² = u² + 2as, or s = ((u + v) / 2)t. These equations require constant acceleration and consistent units.
• Graph interpretation: Questions may ask for velocity from the slope of a position-time graph, acceleration from the slope of a velocity-time graph, or displacement from the area under a velocity-time graph. A horizontal velocity-time graph must be identified as constant velocity and zero acceleration.