Introduction to Motion

Describing Motion

Motion is the change in position of an object with respect to its surroundings over time. Describing motion accurately is the first step in understanding the laws of physics that govern it. We use concepts like position, displacement, distance, velocity, and acceleration to quantify and analyze motion.

Motion Along A Straight Line

One-dimensional motion, or motion along a straight line, is the simplest type of motion to describe. It occurs when an object moves along a single axis (e.g., forward/backward on a road, up/down in the air). This simplifies the analysis as we only need to consider one dimension (usually represented by the x-axis).

• Position: The location of an object in space relative to a chosen origin or reference point. It is typically represented by a coordinate value along the line of motion (e.g., $ x $).
• Path Length: The total distance travelled by an object, irrespective of its direction. It is always a non-negative scalar quantity.
• Displacement: The change in position of an object. It is a vector quantity, defined as the final position minus the initial position. If an object moves from $ x_i $ to $ x_f $, its displacement $ \Delta x $ is $ x_f - x_i $. For motion along a straight line, displacement can be positive (moving in the positive direction) or negative (moving in the negative direction).

Example: A car travels 5 km east, then 3 km west.

• The distance travelled (path length) is $ 5 \, \text{km} + 3 \, \text{km} = 8 \, \text{km} $.
• If we define East as positive, the initial position could be 0. The first displacement is $ +5 \, \text{km} $. The final position is then $ +5 \, \text{km} $. The second displacement is $ -3 \, \text{km} $. The final position is $ +5 \, \text{km} - 3 \, \text{km} = +2 \, \text{km} $ (meaning 2 km east of the origin). The net displacement is $ +2 \, \text{km} $.

Uniform Motion And Non-uniform Motion

The distinction between uniform and non-uniform motion lies in how the velocity changes over time.

Uniform Motion

An object is said to be in uniform motion if it travels in a straight line with a constant velocity. This means:

• The object covers equal distances in equal intervals of time.
• The velocity (both speed and direction) remains constant.
• The acceleration is zero ($ \vec{a} = 0 $).

For uniform motion in one dimension:

If an object starts at position $ x_0 $ at time $ t=0 $ and moves with constant velocity $ v $, its position at any time $ t $ is given by:

$ x(t) = x_0 + v t $

This is a linear relationship between position and time.

Non-uniform Motion

An object is in non-uniform motion if its velocity changes over time. This change in velocity can be due to a change in speed, a change in direction, or both.

• The object does not cover equal distances in equal intervals of time.
• The velocity is not constant.
• The object has acceleration ($ \vec{a} \neq 0 $).

Non-uniform motion is further categorized based on how the velocity changes:

• Uniformly Accelerated Motion: The velocity changes at a constant rate (constant acceleration).
• Non-uniformly Accelerated Motion: The acceleration itself changes with time.

Example: A car starting from rest and speeding up is in non-uniform motion (specifically, uniformly accelerated motion if it speeds up at a constant rate). A car moving around a circular track at a constant speed is also in non-uniform motion because its direction is continuously changing, hence its velocity is changing.