Measuring Motion

Observing Motion

• Motion: When an object changes its position with respect to a frame of reference.

• Frame of Reference: Usually a stationary object, such as the Earth, against which motion is compared.

Direction and Distance

• Motion can be described using reference directions: north, south, east, west, etc.

• To describe motion accurately, both distance and direction are necessary.

• Distance: Length of the path an object takes.

• Displacement: Shortest distance from starting point to ending point.

Key Differences

• Distance: Measures total path length.

• Displacement (s): Measured using the shortest line between two points. For example:

  • If John walks from point A to B to C, his distance is the total path traveled, while his displacement is the straight line from A to C.

Examples and Practice

1. John's Path:

   • Distance: total meters walked.

   • Displacement: the straight distance from A to C.

2. Football Coach:

   • The coach moves between positions A, B, C, and D. Displacement is calculated between the first and last points.

Speed vs. Velocity

Speed

• Definition: How fast an object moves; calculated as distance traveled over time.

• Formula:

  • Speed = Distance / Time

  • Example: If a car travels 60 miles in 2 hours, Speed = 60 miles / 2 hours = 30 mph (average speed).

• Instantaneous Speed: Speed at a specific moment (e.g., car speedometer).

Velocity

• Definition: Speed in a given direction. For instance, 20 m/s to the east.

• Velocity is directional and varies based on frame of reference.

• Positive velocity indicates movement in one direction; negative velocity indicates the opposite.

Resultant Velocity

• When two objects move together, their velocities can add or subtract depending on their directions.

• Example Problem: If a plane and wind are moving in the same direction, calculate resulting velocity by sketching or calculating.

Graphing Motion

• Motion can be graphically represented.

• Distance vs. Time Graph (y-axis: distance, x-axis: time):

  • The slope of the graph indicates an object’s speed.

  • Linear slope for constant speed; curves indicate changing speed.

• To find instantaneous speed at a particular point (e.g., 2.5 seconds), calculate the slope of the tangent line at that point.

Practice Problems

1. Find velocity of a swimmer covering 110 m towards shore in 72 s.

   • Formula: Velocity = distance/time.

   • Result: 110 m / 72 s = 1.53 m/s towards shore.

2. Find velocity of a baseball thrown 38 m in 1.7 s.

   • Result: 38 m / 1.7 s = 22.35 m/s.