Question

If someone runs for 20 minutes at 5 km/h east then turns around and runs 30 minutes at 3 km/h west along the same path, what is their average speed and velocity?

Answer 1

Hi! Do you know the main difference between speed and velocity?

Answer 2

Um, Velocity is a vector measurement and speed is a scalar, right? and you need a distance thing for velocity... right?

Answer 3

Right! Vector means that direction matters! So, if you change direction, the velocity will really be affected. The speed is just a simple average of the magnitudes.

Answer 4

So, you go east and then west.

Here's something to make velocity easy. Since we need direction, we'll say east is positive and west is negative.

Answer 5

alright, so that makes sense.. but how do i figure out how far the person is going in either direction?

Answer 6

You could do that, if you wanted, but you don't have to. There is the \(v=\dfrac{d}{t}\) equation.

Or, the average velocity is like...
The velocity, multiplied by its time duration, plus another velocity times its duration, all divided by the total time duration. I think that works!

Answer 7

But how do i find the displacement or distance?

Answer 8

I'm not sure if your professor had a particular way of solving this or not, sorry!

I have to go, sorry, but I'll be back by tomorrow! Just remember to use positive and negative for direction! If the average is positive and you keep east positive, you want to say the average velocity is east!!

Also, the speed does not involve different directions, so no different signs! All positive! (The absolute value of the velocity's magnitude)
:)

Answer 9

Alright, thank you for your help! (:

Answer 10

Oh, I didn't know you'd need to find those!

Use \(v=\dfrac{d}{t}\implies d=vt\) where \(d\) is displacement, \(t\) is time, and \(v\) is velocity. If you want the speed, then \(d\) is distance and \(v\) is speed - just don't use signs!

Answer 11

Good luck!

Answer 12

Thank you!