The Possible Wrongness...

[googol]

I have two questions that need to be answered.

1. Is there such thing as Instantaneous Speed? S = D/T, so if it were instantaneous: t = 0.

2. My current science teaching claimes that forces must be balanced to move at a constant velocity, otherwise the object will accelerate. When he drew a free body diagram of a parachuter (Can't Spell) Thee Forces of Wind Resistance and Gravity were equal, but wouldn't that mean he would be suspended? I think that if forces are balanced the object will not move and an imbalance will cause a constant velocity.

[OfficeShredder]

force=mass*acceleration. So if the forces balance, there is no net acceleration. Since the parachuter was accelerating before the forces balanced (since wind resistance is proportional to velocity, and he started off moving slower), he'll continue moving at his current velocity, since he isn't accelerating.

For the first question, you've misinterpreted instantaneous velocity. Instantaneous velocity is the velocity one is moving at at a given point in time. For example, the spedometer on your car (theoretically) shows instantaneous velocity. In terms of calculations, it's mostly used in calculus, because it happens to be the derivative of distance.

Although you should notice that if v=d/t, if t=0, shouldn't d=0 too? This is the basic essence of the derivative, taking the limit as both d and t approach 0.

[HallsofIvy]

IF an object has 0 velocity and there are no forces on it, then it will remains stationary. But that can't happen in the situation you describe: wind resistance forces are depend upon velocity. If an object has 0 velocity, then it has NO wind resistance forces to offset gravity and will accelerate downward. What your teacher was talking about, I think, is "terminal velocity"- an object will accelerate downward due to gravity until the wind resistance forces become enough to offset gravity and then it will no longer accelerate. But that doesn't mean its velocity is 0. One of Galilleo's laws said "If an object has no net force on it, it will continue to move in a straight line at constant velocity." That was incorporated in to Newton's laws as "F= ma": no force, no acceleration. But the velocity remains constant.

You need to work on the difference between "acceleration" and "velocity".

Yes, there is such a thing as "instantaneous velocity": at each instant, an object is moving! Your formula, V= s/t, is only true for constant velocity. If you know the velocity is constant, you can take t to be anything and know that the velocity over a range of distance will be the same and the instantaneous velocity. If the velocity is not constant, that formula does not work and you must use calculus.