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Why can't i apply the simple average velocity formula?

by rainstom07
Tags: apply, average, formula, simple, velocity
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rainstom07
#1
Jan30-12, 04:06 PM
P: 16
I'm doing a homework problem (i already know the answer) and i came across an error in my logic/application of the formula Vavg = (v + v0)/2. Hopefully you can help me understand why it's incorrect to use the formula.

x = 12t2-2t3 describes a particle position. the derivative of x = 24t-6t2.

The homework question asked me find the average velocity between t = 0 and t = 3.

Using the formula Vavg = Δx/Δt yields 18 m/s... the correct answer.

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When i use the simpler formula: Vavg = (vf + vi) / 2 = (x'(3.0)+x'(0.0))/2 = 18/2. I get 9 m/s which is incorrect.

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Adding the velocity at t=3 with the velocity at t=0 and then dividing by 2 should've produced 18 m/s... My logic is clearly wrong, but how?

x' describes the velocity of the particle at t seconds? right?

thanks.
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Studiot
#2
Jan30-12, 04:31 PM
P: 5,462
Hello rainstom, welcome to Physics Forums

Your average forumla (t0+t3)/2 is only correct if x is a linear function of t ie a straight line.

The function x = 12t2-2t3 is decidedly non linear

The way to derive an average for a non linear function (works for linear as well but is trivial) is to integrate the function and divide by the interval or number of points or samples.

So average = Area/Interval

Does this help and can you now obtain the correct answer?
rainstom07
#3
Jan30-12, 04:42 PM
P: 16
Your average forumla (t0+t3)/2 is only correct if x is a linear function of t ie a straight line.
Thank you! i knew there was some sort of condition attached to the simpler version of average velocity.

Does this help and can you now obtain the correct answer?
^^ yup

willem2
#4
Jan30-12, 05:58 PM
P: 1,395
Why can't i apply the simple average velocity formula?

Quote Quote by Studiot View Post
Hello rainstom, welcome to Physics Forums

Your average forumla (t0+t3)/2 is only correct if x is a linear function of t ie a straight line.

The function x = 12t2-2t3 is decidedly non linear
I suppose you meant v_avg = (v_0 + v_3)/2 is only correct if v is a linear function of t.?

X must then be a quadratic function of t, and x = 12t2-2t3 isn't a quadratic.
Studiot
#5
Jan30-12, 06:31 PM
P: 5,462
Hello willem2 does this attachment help?

The average velocity is the number which if you multiplied it by the time would give you the total distance travelled.
Attached Thumbnails
average1.jpg  


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