# Instantaneous velocity from avg velocity with constant accelartion

#### KeilB

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.

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#### Ninty64

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

#### KeilB

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.

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