Unit_02_Kinematics_I_Uniform

Representing Uniform Motion

Graphs

Position vs. Time Graphs

1) slope = (d₂ - d₁) / ( t₂ - t₁) = change in position /change in time = Dd / Dt = velocity

2) For uniform motion, the graph appears to be a straight line with a constant slope and a constant velocity. A steeper slope indicates a larger velocity.

3) For non-uniform motion, the slope changes. As the velocity increases, the slope increases. As the velocity decreases, the slope decreases

Velocity vs. Time Graphs

For uniform motion, the graph appears to be a horizontal line with a slope of zero. Uniform motion with a higher velocity has a larger y intercept than uniform motion with lower velocity.

3) For non-uniform motion, changes in velocity are recognized by segments of the graph that are not horizontal.

Analysis of Graphs

1) Calculate the velocity by taking the slope of a position Vs. time graph.

2) Given a position vs. time graph, draw the corresponding velocity vs. time graph.

3) Given a velocity vs. time graph, draw the corresponding position vs. time graph.

4) Given a position vs. time graph determine the instantaneous velocity at a given time by

selecting the point on the graph

drawing a tangent line to that point

taking the slope of the tangent

5) Given a velocity vs. time graph, determine the instantaneous velocity at a given time by

selecting the point on the graph that corresponds to the time

reading over to the y axis to determine the velocity

6) Determine the average velocity from a position vs. time graph by

selecting the block of time

connecting the two points at either end and drawing a line between them

taking the slope of that line

Motion Maps

Any motion can be represented using motion maps. Motion maps consist of points which represent both position and time. Arrows represent the velocity. The length of the arrow is proportional to the velocity.

Kinematics Problems using v = Dd / Dt

1) Simple problems where two out of the three variables are given and you have to solve for the third.

2) More complicated problems involving

multiple conversions

"catch up problems"

"meeting problems"

Resources