Distance, position, and displacement

Describing objects' motions

Physicists use exclusive terms to describe the motion of objects, some are already known.

• As said earlier, kinematics refers to the study of how objects move.

• Motion = change of an object's location, measured by something.

• Distance (d), in physics = total length of travelled distance by an object in question, metre as the base unit.

• Direction is expressed in degrees on a compass or directions (north, south, west, or east) or as up, left, down, or right. It's crucial to describe something's motion.

E.g. 500 m [E] says that something is in 500 metres toward east 

Scalar and vector quantities

A scalar is a quantity with only magnitude (size).

A vector is a quantity with both magnitude and direction. Like limiting slope in math (which are under), it has above its symbol for a variable representing a vector quantity.

Positions and displacement

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As implied, the position (d) is an object's distance and direction from a certain reference point.

Displacement is a straight line/distance going in certain directions (north, south...)

The arrow above the position's symbol, d, indicates the vector: it has a direction and a magnitude. 

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If an object moves more than once, its total displacement ΔdT is determined by adding the displacements with the equation:

Problem 3

A dog leaves her trainer and runs 80 m due west to pick up a ball, before dropping it into a bucket 27 m due east. What's the dog's total displacement?

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Solution: d1 - d2 = Δd (total displacement) 

80 m [W] - 27 m [E] = 107

Vector scale diagrams

Vector scale diagrams are another way to solve displacement problems, showing the vector linked with a displacement drawn to a certain scale. 

They can be represented by a directed line segment, a straight line between points with a specific direction, which only have magnitudes.

Vector diagrams show motion using line segments with arrowheads to show specific directions, useful to measure objects' total displacements from its original position. 

Directed line segments are line segments with arrowheads.

An arrowhead's end is the "tip". 

Its other end is the "tail". 

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E.g. AB is a line segment in the direction from A to B.

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E.g. Consider 2 displacements: Δd1 = 700 m [W] and Δd2 = 500 m [W]. 

The total displacement by adding the vectors can be determined by drawing a vector diagram. 

The larger a vector scale diagram, more precise results it'll be.