Postby **gorcee** » Tue Oct 07, 2008 8:24 pm UTC

So, a constant velocity means that the skier has zero acceleration.

That means his distance traveled over time is basically his speed times the time he skis. Just like if you're in a car doing 30 km/h for 2 hours, you go 60 km. If you know calculus, then this is the integral of the velocity.

Now acceleration is slightly trickier. Acceleration means that the skier is going faster and faster all the time. So the distance traveled is the integral of the velocity, which itself is the integral of the acceleration.

A way to look at the question is, "how FAST is the second skier going after T seconds?" Well, you handle this just like you handled the first problem. Multiply his acceleration (meters per second squared) by the time (seconds). Units cancel just like numbers. m/s^2 * s = m/s.

Then you have a profile of his velocity over time. So it starts off small, but gets bigger and bigger. This is OK. Just multiply the new relation for his velocity by time, and you have the distance!

This is only the first step in understanding. We don't KNOW how long or how far the 2 skiers travel before meeting. All we know is they meet somewhere. Let's call that distance D and the amount of time it takes T. Since both skiers are going D meters, set the two equations obtained equal to each other, and cancel out, and you should have an easy to solve quadratic equation.