Kinematics: Motion in One Dimension

Uniform Motion

Uniform motion describes the movement of an object at a constant velocity, meaning both speed and direction remain unchanged over time. This is the simplest form of motion and serves as a foundation for understanding more complex motion.

• Definition: Uniform motion occurs when an object moves equal distances in equal intervals of time, without changing direction.

• Motion Diagram: In a motion diagram, the displacements between successive frames are equal, indicating constant velocity.

• Position-Time Graph: The graph of position versus time for uniform motion is a straight line. The slope of this line represents the velocity.

• Average Velocity Formula: or where (or ) is the change in position and is the change in time.

Relating Position and Velocity Graphs

Position and velocity graphs are closely related in kinematics. The slope of the position-time graph at any interval gives the value of velocity for that interval.

• Example: If the position graph has a slope of from to s, the velocity graph will show a value of for that interval.

• Interpretation:

  • Positive slope: Object moves in the positive direction.

  • Negative slope: Object moves in the negative direction.

  • Zero slope: Object is stationary.

Mathematics of Uniform Motion

The mathematical description of uniform motion allows us to predict an object's position at any time, given its initial position and constant velocity.

• Key Formula: where:

  • = final position

  • = initial position

  • = constant velocity

  • = time interval

• Application: This formula is used to calculate the position of an object after a certain time has elapsed, assuming constant velocity.

Distance Traveled vs. Displacement

Distance and displacement are two important concepts in kinematics, often confused but fundamentally different.

• Distance Traveled: The total length of the path taken by the object, regardless of direction.

• Displacement: The straight-line change in position from the initial to the final point, including direction.

• Example: If an ant zig-zags back and forth on a picnic table from 0 cm to 50 cm, the distance traveled could be 50 cm (total path), while the displacement is the net change in position (e.g., 50 cm if it ends at 50 cm, or -30 cm if it ends at 20 cm).

Additional info:

• Displacement is a vector quantity (has magnitude and direction), while distance is a scalar (only magnitude).

• In uniform motion, displacement and distance are equal if the motion is in a straight line without changing direction.