Chapter 2.1 to 2.3 Kinematics in One Dimension AP Physics C

Points vs. Function

Interpreting a Position Graph

Uniform Motion

The Math of Uniform Motion

Skating with Constant Velocity (vx)A = DxA/DtA =“rise”/“run” = (2.0 m)/(0.40 s) = 5.0 m/s DxB = (0.0 m) - (1.0 m) = -1.0 m (vx)B = DxB/DtB = (-1.0 m)/(0.50 s) = -2.0 m/s Reality check: (vx)A = 5.0 m/s » 10 mph (vx)B = -2.0 m/s » -4 mph Reasonable.

Motion Diagrams Position Velocity

Instantaneous Velocity Position A jet plane accelerates for takeoff

Using Motion Diagrams Instantaneous velocity is the local slope of the curve. Observation: Any smooth curve becomes linear at a sufficiently high magnification.

Velocity from Graphical Position ay>0 ay<0

Welcome to Calculus… This is the Derivative!!!

Multiple Choice Question Which of the green velocity vs. time graphs goes with this blue position vs. time graph?

Finding Position from Velocity The figure shows the velocity of a drag racer. How far does the racer move during the first 3.0 s? Solution: The net distance traveled is the area under the velocity curve shown in blue. This is a triangle with sides 12 m/s and 3.0 s. The area of this triangle is: A = ½(12 m/s)(3 s) = 18 m. Thus, the drag racer moves 18 m in the first 3 seconds.

Welcome to Calculus… This is the Integral!!! Formal way to write this (don’t need to know this yet): Conceptual way to think about this:

Finding the Turning Point The figure shows the velocity of a particle that starts at xi= 30 m at time ti=0 s. 10 Draw a motion diagram for the particle. Where is the particle’s turning point? At what time does the particle reach the origin? 10 10 10 10 Solution: The figure shows the motion. The particle has zero velocity at t=2 s, which must be its turning point. Its position is x = x0 + 0∫2 v dt = 30 m + area of triangle from 0 to 2 s = 30 m + ½(10 m/s)(2 s) = 40 m. To get to the origin, the particle must move -40 m from the turning point. This occurs at 6 s (see diagram).

Multiple Choice Question Which of the blue position vs. time graphs goes with this green velocity vs. time graph? The particle’s position at ti = 0 s is xi = -10 m.