Calculating Average Speed for a Trip: A Physics Challenge

[Niki Lively]

1. You plan a trip on which you want to average 90 km/hr. You cover the first half of the distance at an average speed of only 48 km/hr. What must your average speed be in the second half of the trip to meet your goal? Note that the velocities are based on half the distance, not half the time. Is this reasonable?


2. Not sure.



3. This is the beginning of something new. Our Physics class has started a couple weeks ago, so my fellow classmates & I are still settling into the new concept of our first Physics class; our first time allowed to think "outside the box". I'm very intrigued, but confused. As I said, this is something new in the chapter, & he hasn't given us many details on where to start. I just am confused with which sort of formula to use. I thought back to previous math, & I'm thinking along finding the median. So, I thought about what would work out to divide by 2 to get 90; obviously 180. 48-180=132. So, 132 km/hr would have to be the average speed for the second time...? I know I can't possibly be correct. It's probably something quite obvious that I'm just not catching. So, can someone help me by giving me the proper formula so I can figure it out? I'm just not sure on where to place what... I know conversion formulas, but that is irrelevant right now. Any help would be greatly appreciated.

 

[AEM]

1. You plan a trip on which you want to average 90 km/hr. You cover the first half of the distance at an average speed of only 48 km/hr. What must your average speed be in the second half of the trip to meet your goal? Note that the velocities are based on half the distance, not half the time. Is this reasonable?


2. Not sure.



3. This is the beginning of something new. Our Physics class has started a couple weeks ago, so my fellow classmates & I are still settling into the new concept of our first Physics class; our first time allowed to think "outside the box". I'm very intrigued, but confused. As I said, this is something new in the chapter, & he hasn't given us many details on where to start. I just am confused with which sort of formula to use. I thought back to previous math, & I'm thinking along finding the median. So, I thought about what would work out to divide by 2 to get 90; obviously 180. 48-180=132. So, 132 km/hr would have to be the average speed for the second time...? I know I can't possibly be correct. It's probably something quite obvious that I'm just not catching. So, can someone help me by giving me the proper formula so I can figure it out? I'm just not sure on where to place what... I know conversion formulas, but that is irrelevant right now. Any help would be greatly appreciated.

Sometimes you can get a feel for how a problem works if you make up a simple example. The equation that applies here is s = vt where s is the distance, v is the velocity and t is the time. Suppose, for example you wanted to go 90km. at an average speed of 90 km/hr that would take you 1 hour. The problem said you travel the first half of the trip at an average velocity of 48 km/hr. That means it took

$$t = \frac{s}{v} = \frac{45}{48} = \frac{15}{16} hour$$

To achieve your desired goal of averaging 90 km/hr for the whole trip you would have to travel the last 45 km in 1/16 of an hour or 3 and 3/4 minutes. I think you might get a speeding ticket!

 

[nlightner]

Hello! I can provide some guidance on how to approach this problem.

First, it is important to understand what average speed means. Average speed is the total distance traveled divided by the total time taken. In this case, we are given the average speed for the entire trip (90 km/hr) and the average speed for the first half of the trip (48 km/hr).

To find the average speed for the second half of the trip, we can use the formula: Average speed = total distance / total time. Since we know the average speed for the entire trip and the average speed for the first half, we can set up an equation:

90 km/hr = total distance / total time

We know that the total distance is equal to the distance traveled in the first half (which is half of the total distance) plus the distance traveled in the second half (also half of the total distance). So we can write:

90 km/hr = (1/2) total distance / (1/2) total time

Simplifying, we get:

90 km/hr = 2 x (total distance / total time)

We already know that the average speed for the first half of the trip is 48 km/hr, so we can plug that in:

90 km/hr = 2 x (48 km/hr + x) where x is the average speed for the second half of the trip.

Solving for x, we get:

x = (90 km/hr - 48 km/hr)/2 = 21 km/hr

So, the average speed for the second half of the trip would need to be 21 km/hr in order to meet the goal of averaging 90 km/hr for the entire trip.

As for whether this is reasonable, it depends on the distance and time taken for the first half of the trip. If the first half of the trip was significantly longer than the second half, then it may not be realistic to expect an average speed of 21 km/hr for the second half. However, if the first half and second half were roughly equal in terms of distance and time, then it is possible to achieve an average speed of 21 km/hr in the second half of the trip.

I hope this helps clarify the problem and gives you a starting point to solve it. Best of luck in your Physics class!