Avg Velocity Calculation: San Antonio-Houston & Back

[pseudonewtonian]

Average velocity ?

You're driving an interstate 10 from Sn Antonio to Houston half the time at 55km/hr and the other half at 90km/hr . What is your average speed a) from San Antonio to Houston b) from Houston back to San Antonio c) for the entire trip ? What is your average velocity for the entire trip ? Indicate how average velocity can be found on a sketch of x versus t ?

HI I'm new to the forums and this question has me all confused... Any help is greatly appreciated. Thanks in advance.

 

[Galileo]

The average speed over some time interval T is (distance travelled)/T
You know you traveled 55 km/hr for a period of T/2
and 90 km/h for the remaining period of T/2.
With this you can find the total distance travelled.

 

[HallsofIvy]

If you do not know the answers to a) and b) you have a serious problem! Run, do not walk to your instructor and throw yourself on his/her mercy.

The answer to c) depends upon whether you really mean "velocity" rather than "speed" (do you know the difference?). If it really is "velocity" (and you know the distinction between "speed" and "velocity") the problem is trivial.

If you really mean the "average speed", then you will have to know the distance between San Antonio and Houston. That CANNOT be calculated from the information given here- you may have to consult a map! I notice that one speed is given in "miles per hour" and the other in "kilometers per hour". If you find the distance in miles, you will want to convert " 60 kilometers per hour" to "__ miles per hour". If you find the distance in kilometers, you will want to convert the other way. Once you know the distance, how long (time) does it take to drive from San Antonio to Houston at 55 mi/hr? How long does it take to drive from Houston to San Antonio (same distance of course) at 60 km/hr. What is the total time taken to drive the total distance (twice the distance from San Antonio to Houston)?

 

[UrbanXrisis]

If you do not know the answers to a) and b) you have a serious problem! Run, do not walk to your instructor and throw yourself on his/her mercy.

 

[pseudonewtonian]

consult a map... ? Thats not given in the problem.. and i got a serious problem u say ? Well u might be right. I still do not understand what to do... This sum is from Fundamentals Of Physics - Resnick Halliday Walker 1st chapter.. and by the way i missed out on some info... ie.. On the way back from Houston u drive at 55km/hr for half the distance and 90km/hr for the other half... this should've been there before the questions

 

[ek]

consult a map... ? Thats not given in the problem.. and i got a serious problem u say ? Well u might be right. I still do not understand what to do... This sum is from Fundamentals Of Physics - Resnick Halliday Walker 1st chapter.. and by the way i missed out on some info... ie.. On the way back from Houston u drive at 55km/hr for half the distance and 90km/hr for the other half... this should've been there before the questions

A and B really are pretty darn easy questions. They're not even really physics.

You have six apples and I have four apples, what is the average number of apples we each have?

 

[pseudonewtonian]

ya you i get it ek... and i know the difference between physics sums and apples... that's ok... i know how to do it that way but is that quite right physically ? Thats my problem I don't get the physical significance of it otherwise average is kid's play.. btw this is not my homework or anything so i aint being lazy... kinematics is driving me mad

 

[ek]

There's nothing more to it than that.

55 + 90 / 2

So if the distance between the two cities was 290km, then it would take 4 hours.

55 km/hr for 2 hrs = 110 km
+
90km/hr for 2 hrs = 180 km
290 km in four hours.
290/4 is 72.5km/hr, just like the original equation.

 

[primarygun]

May I know how old is a Grade K-12 student?

 

[ek]

May I know how old is a Grade K-12 student?

K -> Kindergarten -> 5 years old.

12 -> Grade 12 -> 16/17/18 years old.

K-12 is every age in between.

 

[primarygun]

Oh so I am not in G-12 lol

 

[BobG]

consult a map... ? Thats not given in the problem.. and i got a serious problem u say ? Well u might be right. I still do not understand what to do... This sum is from Fundamentals Of Physics - Resnick Halliday Walker 1st chapter.. and by the way i missed out on some info... ie.. On the way back from Houston u drive at 55km/hr for half the distance and 90km/hr for the other half... this should've been there before the questions

Make sure whether the question is saying you drove half the time at a given speed or half the distance at a given speed. Half the time is pretty easy - you just take the average of your speeds. For half the distance, you need to find out how long it took you for the first leg, then how long it took you for the second leg.

And, actually, if you play with the equations, you can find the average speed without knowing the distance, even in the second case.

$$t_{tot}=\frac{d}{s_1}+\frac{d}{s_2}$$

or

$$t_{tot}=\frac{ds_2 +ds_1}{s_1s_2}$$

$$s_{ave}=\frac{2d}{t_{tot}}$$

The distance winds up canceling out.