Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
If a freely falling body starts from rest, then its displacement is given by $ s = \frac{1}{2} gt^2 $. Let the velocity after a time $ T $ be $ v_T $. Show that if we compute the average of the velocities with respect to $ t $ we get $ v_{ave} = \frac{1}{2} v_T $, but if we compute the average of the velocities with respect to s we get $ v_{ave} = \frac{2}{3} v_T $.
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Amrita Bhasin
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 2 / BC
Chapter 6
Applications of Integration
Section 5
Average Value of a Function
Campbell University
Oregon State University
University of Michigan - Ann Arbor
Boston College
Lectures
14:18
If a freely falling body s…
01:05
01:52
The motion of a body falli…
07:48
For a freely falling objec…
03:56
Use the distance function …
02:39
Distance. For a freely fal…
recall the fact for this question that velocity is the derivative of position. In other words, ask prime of tea, as indicates position in this context. Therefore, the average lost you with respected teed one over tee times 1/2 This is 1/2 V of tea V s g t can t can be written this just simple algebraic manipulation as V over G. Therefore, V is the square root of two gs. Therefore we know that are average There's one over us Humanist es Juan the integral from us want us to the of STS is the same thing is one of her B minus A. And to grow from a bead on the function we're just using us Want us to in this context, therefore we end up with We're just putting in now what we know and then we have Diaz instead of GTX are variables s and this is a corpulent to 2/3 v of tea
View More Answers From This Book
Find Another Textbook
02:47
One card is selected at random from deck of cards. Determine the probability…
01:01
The critical F value with 6 numerator and 40 denominator degrees of freedom …
02:17
An urn contains 11 red balls and 9 white balls. Two balls are to be selected…
K(3) = Zand 93)=7, wnat is (( ^ 9XJR (+913) = (Bimplify your anster )
05:20
(4 pts ) A line passes through the point (0. and forims an angle of 0 = 5 w…
01:15
Sokie ta aquabon. 6 In Sx = 1802{} 0 B { {os} 0D 3/6}
01:03
Find four angles in different quadrants with the reference angle 30"_
05:15
Gloria would Iike to construct a bOx With volume of exactly 50ft3 using only…
10:06
AnatunalbutJuncd"[UeLaltItom J] 7milon Mn 7uobio[7 e mlliun…
03:33
[-/3 Points]DETAILSFor each of the following functions; determine th…