Describing Motion: Position, Distance, Displacement

• Motion refers to an object's change in position relative to a fixed point, typically the origin (0,0).
• A coordinate system with the origin as a fixed point is used to describe an object's position.

Describing Motion: Where and When

• Describing motion involves knowing where and when an object is located.
• Position describes how far an object is from the origin with direction.
• Position is a vector quantity with both magnitude and direction.
• X is the standard symbol for position.
• The SI unit for position is the meter (m).
• An object's position to the right or above the origin is positive and to the left or below is negative.
• Vector quantities have both magnitude and direction, and position is one of them.

Distance and Displacement

• Distance is the total length of the path traveled by an object, whereas displacement is the change in position of an object.
• Distance is a scalar quantity without direction, and meters (m) is the SI unit.
• Examples of distance units include kilometers (km), centimeters (cm), and millimeters (mm).
• Displacement is a vector quantity calculated as the change in position.
• Displacement = Δx = xf - xi, where xf is the final position and xi is the initial position.
• Displacement depends on the path taken.
• Distance is the value of the path taken, while displacement is the length between two points.

Examples of Distance and Displacement

• When calculating the traveled distance, the whole path is measured
• The displacement depends on the path and direction.
• If an object travels from point A to point B, the distance is 5 m.
• If an object travels from point A to point B and back to point A, the distance is 6m, but the displacement is 0.

Displacement sign convention

• Positive displacement travels to the right.
• Negative displacement travels to the left.

Displacement Examples

• An object goes from point xi = 2 to xf = -3 m, then the displacement is -5m
• An object goes from point xi = -4 to xf = 4 m, then the displacement is 8m

General notes on distance and displacement

• Distance is the entire path length; displacement indicates the net change in position.

Adding and subtracting displacement (vectors)

• Total displacement is achieved by adding/subtracting vectors

Speed and Velocity

• Speed is the rate at which an object covers distance.
• Velocity is the rate at which an object changes position with direction.
• The unit of speed and velocity is meters per second (m/s).
• Examples of speed and velocity units include m/s, km/h, m/s North, and m/s South.
• Speed = total distance / total time, and velocity = displacement / time.
• Average velocity is positive when moving in the positive direction and negative when moving in the negative direction.

Speed Types

• Instantaneous speed is the speed at a specific moment.

Graphing Motion

• Motion over time is shown on a distance-time graph with time on the horizontal axis and distance on the vertical axis.
• Constant speed is represented by a constant increase in distance over equal time intervals in these graphs.
• Position-time graphs display an object's position on the vertical axis over time on the horizontal axis.
• The slope of a position-time graph represents the speed.
• The intersection of two lines on a position-time graph indicates that the objects are at the same position at that time.