Warm up Problem An athlete sprints 50.0 m to the right in 6.00 s, stops and then walks back to the starting line in 40.0 s. Determine a) the average velocity for the sprint b) the average velocity for the walk and c) the average velocity and average speed for the complete round trip?

Physics Honors AB – Day 09/2-09/3

Agenda

Position vs. time If displacement went on the y-axis & t went on the x-axis

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 0.0 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 0.5 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 1.0 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 1.5 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 2.0 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 2.5 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 3.0 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 3.5 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 4.0 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 4.5 s

Position vs. time Every 0.5 s ball moves 1/5 m, until it hits 1m and stops until we stop recording time at 5 s. t = 5.0 s

Position v. time plot

Example Problem A dog runs back and forth in a dog run. It starts from the far left and runs to the right 10 m in 3 s. Then goes back to the left 5 m in 5 s. It stops at that point for 2 s before running to the left 5 m in 3 s. Plot this data in a position v. time plot and determine the velocity for each section.

Representing data as a function

Example problem

Example Problem

Velocity Problem Two runners begin from the same starting point. If the first runner is running with an average velocity of +1 m/s and the second runner sprints with an average velocity of +2 m/s. When will the second runner be 6 m in front of the first runner?

Example Problem You and a friend are at the airport. Your friend is ahead of you and gets onto a moving walkway traveling +4.0 m/s. When you get onto the walkway she is 7 m ahead of you. If your friend is just standing on the walkway and you are walking with a velocity of m/s, will you catch up with her before you get to the end of the 25m long moving walkway.

Imagine a new set of data This data follows quadratic relationship

Position v. time plot

How would you calculate slope of this type of plot?

Position v. time plot How would you calculate slope of this type of plot?

Position v. time plot So what if we kept moving the time interval closer and closer together

Position v. time plot

Displacement v. time plot The line is said to be tangent to the point on the graph

Instantaneous Velocity The velocity at any point in time The slope of the tangent line of any point on the graph Two points on the graph that are really, really, really, really close together.