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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.So this is the vector version, if you care about direction.
The water is flowing west at 5 km/h, parallel to the shore.
What is the velocity of the sailboat relative to ground, and what is the angle of travel that the sailboat makes with respect to the shore?
So velocity, and there's many ways that you might see it defined, but velocity, once again, is a vector quantity.
And you might be wondering, why don't they use D for displacement? And my best sense of that is, once you start doing calculus, you start using D for something very different.
So his velocity is, his displacement was 5 kilometers to the north-- I'll write just a big capital. You have to give the direction for it to be a vector quantity.
Well, let me just write it out, 5 kilometers north-- over the amount of time it took him. You could do the same thing if someone just said, what was his average speed over that time?(Answer: 13.45 km/h, 48.01 degrees or 41.99 degrees) Problem # 5 If a sprinter runs 100 m in 10 seconds, what is his average velocity?(Answer: 10 m/s) Problem # 6 The world record for the men's marathon is .Solution Problem # 9 The seals around an engine piston are designed for a maximum velocity of 5 m/s relative to the piston wall.If the piston oscillates sinusoidally with a stroke length of 20 cm, what is the maximum engine RPM?Assume there is no friction between merry-go-round and ball.The merry-go-round is rotating at a constant angular velocity of w radians/second, and the ball is released at a radius r from the center of the merry-go-round.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.What is the velocity of the sailboat relative to the woman and what angle of travel does the sailboat make with respect to her?