Braindead - Simple Physics Help

[megaforcetkd]

Homework Statement

A car averages 80 km/h traveling from A to B, and then on the return trip the car averages 60 km/h from B to A. Write the average speed of the car, V, as a function of x, where x is the distance from A to B.

Homework Equations

Not sure what to use.

The Attempt at a Solution

Vavg = [80 km/h(x) + 60 km(x)]/2

Obviously it's wrong =/

 

[Leong]

you must understand that the average speed in this context means the total distance divided by the time taken to cover that distance.
the average speed here doesn't mean the arithmetic mean that we usually learn in mathematics.

 

[megaforcetkd]

The question doesn't provide the time though, and the function needs to be written as a function of the distance.

 

[Leong]

speed = distance/time
you know the average speed for the go and return journeys and the distance is the same. so you can express the TOTAL time to cover both the journeys in term of the distance x.

 

[HallsofIvy]

speed= distance/time=> time= distance/speed

Of course, the total distance is 2x.

 

[megaforcetkd]

I have to express it as V(x) though so I have to express Speed in terms of distance. This is for Pre-Calc, btw. I did all the mechanics things in AP Physics but this is unrelated, right? I've been trying for a while but I still can't get it =/..

I know I can express it in terms of time as T = ((x)/(80kph)) + ((x)/60kph))..

 

[learningphysics]

I have to express it as V(x) though so I have to express Speed in terms of distance. This is for Pre-Calc, btw. I did all the mechanics things in AP Physics but this is unrelated, right? I've been trying for a while but I still can't get it =/..

I know I can express it in terms of time as T = ((x)/(80kph)) + ((x)/60kph))..

That's right. That's the total time for the trip. What's the total distance in terms of x?

 

[megaforcetkd]

2x = ((x)/(80kph)) + ((x)/60kph))(speed).. what do i put for speed?

 

[learningphysics]

2x = ((x)/(80kph)) + ((x)/60kph))(speed).. what do i put for speed?

Solve this expression for speed.

 

[megaforcetkd]

OH so...

Vavg = (2x)/((x)/(80kph)) + ((x)/60kph)).

 

[learningphysics]

OH so...

Vavg = (2x)/((x)/(80kph)) + ((x)/60kph)).

Yup. That's right. You can simplify.

 

[megaforcetkd]

AHHHH! Ok thanks :D. I guess I just wasn't thinking =/ We did this first day of AP Physics.

 

[learningphysics]

AHHHH! Ok thanks :D. I guess I just wasn't thinking =/ We did this first day of AP Physics.

What did you get as the final answer?

 

[megaforcetkd]

68.57 km/h

 

[learningphysics]

68.57 km/h

Yup, that's the answer! Excellent!

 

[megaforcetkd]

YAY! Thanks for the help. Haha you can expect a lot of me though once we start getting into complicated stuff in AP Physics QQ.