*What we are calculating is going to be his average velocity. Sometimes you'll see someone actually put this little triangle, the character delta, in front of it, which explicitly means "change in." It looks like a very fancy mathematics when you see that, but a triangle in front of something literally means "change in." So this is change in time. And you have to be careful, you have to say "to the north" if you want velocity.*

*What we are calculating is going to be his average velocity. Sometimes you'll see someone actually put this little triangle, the character delta, in front of it, which explicitly means "change in." It looks like a very fancy mathematics when you see that, but a triangle in front of something literally means "change in." So this is change in time. And you have to be careful, you have to say "to the north" if you want velocity.But don't worry about it, you can just assume that it wasn't changing over that time period. So he goes 5 kilometers north, and it took him 1 hour. If someone just said "5 kilometers per hour," they're giving you a speed, or rate, or a scalar quantity.(Answer: 11.18 km/h, 63.43 degrees or 26.57 degrees) Problem # 4 In problem # 3, a woman is running at 4 km/h along the shore in the opposite direction to the water's flow.*

On this page I put together a collection of velocity problems to help you understand velocity better.

The required equations and background reading to solve these problems is given on the kinematics page.

If there is a wind blowing at 80 km/h in the direction opposite to take off, what velocity must the plane reach relative to ground in order to take off.

(Answer: 220 km/h) Problem # 8 of the ball relative to the merry-go-round so that, relative to the child, the ball goes around in a perfect circle as he’s sitting on the merry-go-round.

So this is rate, or speed, is equal to the distance that you travel over some time.

So these two, you could call them formulas, or you could call them definitions, although I would think that they're pretty intuitive for you.

So one, let's just review a little bit about what we know about vectors and scalars. So the velocity of something is its change in position, including the direction of its change in position.

So they're giving us that he was able to travel 5 kilometers to the north. So you could say its displacement, and the letter for displacement is S.

And so you use distance, which is scalar, and you use rate or speed, which is scalar. Now with that out of the way, let's figure out what his average velocity was. Because it's possible that his velocity was changing over that whole time period.

But for the sake of simplicity, we're going to assume that it was kind of a constant velocity. So this is equal to, if you just look at the numerical part of it, it is 5/1-- let me just write it out, 5/1-- kilometers, and you can treat the units the same way you would treat the quantities in a fraction. Or you could say this is the same thing as 5 kilometers per hour north. So that's his average velocity, 5 kilometers per hour.

## Comments Solving Velocity Problems

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