Physics question, Vf - Vi / 2 = Vavg?

Question

I just had a physics test and there was a question on the test that I thought was unanswerable. Please read the question and let me know if there is a way to find this.

This is the exact word for word question from the test...
"An airplane is moving 50 km/h and accelerated up to 200km/h before liftoff. Find the average speed of the airplane before liftoff."

Before you answer telling me this is an easy question this is what my teacher said.

I asked if there was any other variables either time or distance. He said I didn't need anything else to figure it out. I asked if the plane was traveling at a constant speed, he said it didn't matter.

I know Vf - Vi / 2 will give me Vavg but I thought that it only applied one something was going at a constant rate.

PLEASE HELP

Answer 1

Vavg = (Vf + Vi)/2 (note, it's a +, not a -) in any case of constant acceleration.



If by "going at a constant rate" you mean the velocity is constant, then Vavg, Vf and Vi are all the same number. This is a special case of constant acceleration with acceleration = 0.

Answer 2

You cannot use a naive definition of average when working with average speed.



Average speed is by definition, total distance traveled divided by total time spent traveling.



You truly need more information. At least you need information if the acceleration is constant during this interval of speed up.



If and only if the acceleration is constant, then you can make use the naive formula for average speed, as you normally take an average. BUT...averages are NOT defined as difference divided by two. Averages are defined as SUM divided by total count of items. In the case of two items, average is SUM divided by two.



Thus:

Vavg = (Vf + Vi)/2





Proof for the case of constant acceleration:



Distance kinematics formula (derived from calculus):

Vf^2 = Vi^2 + 2*a*d



Time kinematics formula, definition of acceleration:

a = (Vf - Vi)/t



Solve equations for d and t:

d = (Vf^2 - Vi^2)/(2*a)

t = (Vf - Vi)/a



Definition of average speed:

Vavg = d/t



Thus:

Vavg = ((Vf^2 - Vi^2)/(2*a))/((Vf - Vi)/a)



Cancel acceleration:

Vavg = (Vf^2 - Vi^2)/(2*(Vf - Vi))



Numerator is a difference of perfect squares. It thus simplifies:

Vf^2 - Vi^2 = (Vf + Vi)*(Vf - Vi)



Cancel factor of (Vf - Vi):



And we get our result:

Vavg = (Vf + Vi)/2

Answer 3

There IS another factor you need to answer this question: Confirmation that the acceleration is constant during the change in velocity. Nowhere in the problem is this stated. If not constant, the formula



Vav = (Vf + Vi)/2



does not apply.

Answer 4

Vavg = (Vf - Vi)/2 + Vi



The (Vf - Vi)/2 term is the average CHANGE in velocity not the avg velocity, itself.



however it is true that => (Vf - Vi)/2 + Vi = (Vf + Vi)/2

Answer 5

we r looking for average so u should have added and divide by 2



(50 + 200)/2 = 125km/hr

Answer 6

V Avg

Answer 7

d