Download presentation

Presentation is loading. Please wait.

Published byAaliyah Hart Modified over 4 years ago

2
Consider the following generalized function of x(t) versus t: Two points P 1 and P 2 on the graph are shown, along with their generalized coordinates. Topic 2.1 Extended C – Velocity in function notation x t x(t)x(t) t1t1 x1x1 t2t2 x2x2 P1(t1,x1)P1(t1,x1) P2(t2,x2)P2(t2,x2) We call the line joining any two points on a graph a secant line. secant line The slope of the secant line is easily found by dividing the rise by the run: t x RISE RUN

3
The average velocity is given by Topic 2.1 Extended C – Velocity in function notation x t x(t)x(t) t1t1 x1x1 t2t2 x2x2 P1(t1,x1)P1(t1,x1) P2(t2,x2)P2(t2,x2) secant line t x RISE RUN The slope of the secant line is the average velocity v = x t Average Velocity Now we're going to simplify our notation a bit, so we don't need subscripts: We begin by calling t 1 just plain "t." t Then t 2 becomes "t + t." t + t

4
The average velocity is given by Topic 2.1 Extended C – Velocity in function notation x t x(t)x(t) x1x1 x2x2 secant line t x RISE RUN v = x t Average Velocity Now, using function notation we can express our two x- values in terms of the t-values: Thus x 1 is the same as x(t). t Then x 2 becomes x(t + t). t + t x(t)x(t) x(t + t) FYI: At first glance it appears that we are making things more complicated. But what we have actually done is we have taken four different values: x 1, x 2, t 1 and t 2, and condensed them into three different values: x, t, and t. And we have eliminated the subscripts.

5
The average velocity is given by Topic 2.1 Extended C – Velocity in function notation x t x(t)x(t) secant line t x RISE RUN v = x t Average Velocity We can now express the average velocity in terms of the three new values: t t + t x(t)x(t) x(t + t) v = x t = x(t + t) - x(t) t Average Velocity function notation

6
Suppose a particle has a position x which can be expressed as x = 2t 2, where x is in meters and t is in seconds. Topic 2.1 Extended C – Velocity in function notation (a) Find the average velocity between t = 1.000 s and t = 1.100 s using the original definition: v = x t Average Velocity x 1 = 2(1.000) 2 = 2.000 m t 1 = 1.000 s x 2 = 2(1.100) 2 = 2.420 m t 2 = 1.100 s t = 0.100 s x = 0.420 m v = x t = 0.420 m 0.100 s = 4.20 m/s

7
Suppose a particle has a position x which can be expressed as x = 2t 2, where x is in meters and t is in seconds. Topic 2.1 Extended C – Velocity in function notation (b) Find the average velocity between t = 1.000 s and t = 1.100 s using the new definition of average velocity: t = 1.000 s v = x(t + t) - x(t) t Average Velocity function notation t + t = 1.100 s x(t) = 2(1.000) 2 = 2.000 m x(t + t) = 2(1.100) 2 = 2.420 m t = 0.100 s v = x(t + t) - x(t) t = 2.420 m - 2.000 m 0.100 s = 4.20 m/s

Similar presentations

Presentation is loading. Please wait....

OK

Motion.

Motion.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on building management system Ppt on age of exploration Ppt on merger and acquisition in india Ppt on surface water flow Ppt on non renewable energy resources A ppt on waste management Ppt on summary writing Ppt on biodiesel in india Ppt on earth movements and major landforms in europe Ppt on cross docking logistics