How Do You Calculate Average Velocity in a Two-Part Journey?

[CrusaderX]

Hi guys, I just started taking physics 2 days ago at my school. One of our questions is:

"You drive a car 2.0 hours at 40km/h, then 2.0 hours at 60 km/h What is your average velocity?"

Ok, from what I understand, Average Velocity is:

delta v = delta distance / delta time

So, To find delta distance, I need to subtract 120 - 80 since 2 hours at 40 km/h is 80 and 2 hours at 60 km/h is 120.

And to get delta time, I'd have to subtract two from two... leaving zero. Well since you can't divide by zero, I'm stuck from here. I've looked at some sites online, but it's not helping me. Can someone help me out here? I'm guessing it's 50km/h from regular average, but I want to make sure.

Thanks in advance!

 

[civil_dude]

You need to think about this. I think you should do this in two parts.

Delta means final - initial, you are correct. But you can't do this all at once because it is NOT contiuous, i.e. the velocity jumps from one magnitude to the other.

So you have to find the initial distance and time, and add this to the next distance and time. I think you should take the total distance and divide it by the total time.

 

[quicknote]

Hi there,

Welcome to the world of physics! It's great that you're already diving into questions and trying to understand the concepts. Let's break down this problem together.

First, let's define average velocity. You are correct in saying that it is the change in velocity (delta v) divided by the change in time (delta t). In this case, the change in velocity would be the final velocity (60 km/h) minus the initial velocity (40 km/h). So, delta v = 60 km/h - 40 km/h = 20 km/h.

Next, we need to figure out the change in time. You correctly identified that the total time for the trip is 4 hours (2 hours at 40 km/h + 2 hours at 60 km/h). However, we can't simply subtract 2 from 2 and get 0. In this case, we need to use the average time, which is the total time divided by the number of segments. So, in this case, the average time would be 4 hours divided by 2 segments, which gives us 2 hours.

Now, we can plug these values into our equation for average velocity:

Average velocity = delta v / delta t = 20 km/h / 2 hours = 10 km/h.

So, your average velocity for this trip would be 10 km/h. This makes sense intuitively, as the car is driving at two different speeds for equal amounts of time, so the average velocity would be the midpoint between those two speeds.

I hope this helps clarify the concept of average velocity for you. Keep up the great work and don't hesitate to ask for help or clarification when needed. Happy learning!