Finding Average Speed and Velocity for a Round Trip

[jedjj]

First let me say hello as this is my first time here. I didn't do well in physics in high school, so most likely I will be on this site a lot for the next year or so. I've never used LaTeX before, but I will try my best to put equations in LaTeX format. I would also like to thank anyone that gives me some kind of direction to go in.

Homework Statement

You drive on Interstate 10 from San Antonio to Houston, half the time at 58 km/h and the other half at 98 km/h. On the way back you travel half the distance at 58 km/h and the other half at 98 km/h.

(a) What is your average speed from San Antonio to Houston?


(b) What is your average speed from Houston back to San Antonio?


(c) What is your average speed for the entire trip?


(d) What is your average velocity for the entire trip?

Homework Equations

$$S_{ave}=\frac{{total distance}}{\Delta t}$$

The Attempt at a Solution

(a) What is your average speed from San Antonio to Houston?
I attained the answer of 78 km/hr. I did this using:
$$S_avg=\frac{S_1+S_2}{2}$$
knowing that
$$S_1=58$$
$$S_2=98$$

I'm really not sure if I did that the way that it was supposed to be done, but it worked as I received an okay with this answer.


(b) What is your average speed from Houston back to San Antonio?

I am stuck here.

I have tried setting the following equations up:

$$S_1=58$$ km/hr
$$S_2=98$$ km/hr
$$T_{1-0}=$$ the time while driving 58 km/hr
$$T_{2-1}=$$ the time while driving 98 km/hr
$$D=$$ the total distance

My thinking is that because I know the speeds, and the distance traveled for both speeds is a constant, I need to find the Ts for each speed.

So I set up the next equations:

$$S_1=\frac{\frac{1}{2}D}{T_{1-0}}$$
$$S_2=\frac{\frac{1}{2}D}{T_{2-1}}$$

therefore; when setting them equal to each other as the distances are the same I get.

$$S_1*T_{1-0}=S_2*T_{2-1}$$

giving:

$$T_{1-0}=\frac{S_2*T_{2-1}}{S_1}$$
$$T_{2-1}=\frac{S_1*T_{1-0}}{S_2}$$

To be honest I have no idea where to go from here, nor do I know if I was even in the right direction. I would greatly appreciate any help here.


(c) What is your average speed for the entire trip?
I believe part b is required here.

(d) What is your average velocity for the entire trip?
I found this to be 0 because displacement is 0

 

[Sourabh N]

you know total time is sum of T1 &T2. Just put T1 & T2 in terms of S1 & S2 in your first eqn.

 

[jedjj]

I have continually tried to figure how to set up the equation, and I cannot figure it out. I'm sorry, but will you please explain a little more?

 

[Sourabh N]

total time = T1 + T2 = ...
Total distance = D
avg speed = total distance/total time. Your have T1 & T2 in terms of D & S1,S2. When you put those values in the eqn for avg speed you'll get avg speed in terms of S1 & S2.(D gets canceled)