Average Velocity of a Car Whilst Braking

[BraedenP]

I don't require an answer to the problem itself, but rather a method I can use to solve it:

Homework Statement

You spot a deer down the road, so you brake to stop before hitting the deer. If your initial speed was 23m/s, what was your average velocity during braking? Deceleration was constant throughout braking.

Homework Equations

v=d/t
a=v/t

The Attempt at a Solution

I can't even begin to solve it, because I'm pretty sure I require an additional piece of data, such as the stopping distance, or the magnitude of the deceleration. Is there a way to solve it without this data?

Any help would be greatly appreciated!

 

[phyzguy]

You don't need any additional data. Try drawing a graph of the velocity vs time, given that the deceleration is constant. What does it look like? What then is the average velocity? Does it depend on the magnitude of the deceleration?

 

[BraedenP]

You don't need any additional data. Try drawing a graph of the velocity vs time, given that the deceleration is constant. What does it look like? What then is the average velocity? Does it depend on the magnitude of the deceleration?

I would do that, but I don't know how long it takes the car to decelerate to 0m/s, because I wasn't given a time, either. If I knew the time, I could solve the problem easily.

I can't graph velocity vs. time without a time to plot against.

 

[phyzguy]

Then try picking a couple of different decelerations, say 23 m/s^2 (in which case it will take 1 second to come to a stop) and 230 m/s2 (in which case it will take 0.1 s to come to a stop). See what you get for the average velocity in these two cases.

 

[BraedenP]

I get 7.5m/s for both of them. However, if I pick some arbitrary number like 540m/s, I get an average velocity of 9.5m/s. For some reason, I'm still not getting how they're related.

 

[phyzguy]

You must not be calculating the average correctly. The point is that if a function changes linearly from an initial value of Fi to a final value of Ff, then the average is just (Fi-Ff)/2. In this case, the velocity changes linearly from 23 m/s to 0 m/s, so the average velocity is just 23/2 = 11.5 m/s, and it doesn't matter what the rate of deceleration is, as long as it is constant.

 

[BraedenP]

You must not be calculating the average correctly. The point is that if a function changes linearly from an initial value of Fi to a final value of Ff, then the average is just (Fi-Ff)/2. In this case, the velocity changes linearly from 23 m/s to 0 m/s, so the average velocity is just 23/2 = 11.5 m/s, and it doesn't matter what the rate of deceleration is, as long as it is constant.

Oh, okay. That makes sense! So basically, it's just like finding the average of any other two magnitudes; the acceleration has no impact on it since it's constant.

Thanks a bunch! I appreciate it.