• Support PF! Buy your school textbooks, materials and every day products Here!

Instantaneous velocity from avg velocity with constant accelartion

  • Thread starter KeilB
  • Start date
2
0
1. Homework Statement
With constant acceleration prove that the average velocity from t1 to t2 =t1 + Δt is equal to the instanous velocity in the middle of the time interval between t1 and t2.


2. Homework Equations
What I am looking for is a general equation that does not involve accelaration. All I have is position. By the way this is 1-D kinematics so no need for vectors.



3. The Attempt at a Solution
Tried all sorts of subs with Vavg= (Vi + Vf)/2 and Vavg= Δx/Δt I tried subbing these in to many of the other equations such as Vf=Vi+at. I imagine there is some sort of trick to it. This thing is driving me nuts.
 
Last edited by a moderator:
46
0
Re: Instananous velocity from avg velocity with constant accelartion

Vavg= (Vi + Vf)/2
Vf=Vi+at
It can be shown this way I believe. Here's a hint:
Vavg= (Vi + Vf)/2
Vavg= (Vi + Vf)/2 - Vi +Vi
Vavg= (Vf - Vi)/2 +Vi
 
2
0
Re: Instananous velocity from avg velocity with constant accelartion

Alright still having a hard time. I got it into that form that you mentioned and was able to get Vavg=2Vf-(3at)/2 which there is a t/2 in there. Good sign I suppose but it just doesn't seem right since I am going to have to use a distance traveled to find it. I will play around with it some more but feel I'm coming to dead ends.
 

vela

Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,461
1,123
Re: Instananous velocity from avg velocity with constant accelartion

Can you express in math what it is exactly that you're trying to show? In other word, what equation says "the average velocity from t1 to t2 is equal to the instantaneous velocity in the middle of the time interval between t1 and t2"?
 

Related Threads for: Instantaneous velocity from avg velocity with constant accelartion

  • Last Post
Replies
1
Views
14K
Replies
8
Views
3K
  • Last Post
Replies
4
Views
6K
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
7
Views
2K
Replies
2
Views
3K
  • Last Post
Replies
2
Views
1K
Replies
3
Views
42K
Top