If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account, is v = mg c (1 − e−ct/m) where g is the acceleration due to gravity and c is a positive constant describing air resistance. (a) Calculate lim t→[infinity] v. 0 What is the meaning of this limit? It is the speed the object reaches before it starts to slow down. It is the time it takes for the object to stop. It is the time it takes the object to reach its maximum speed. It is the speed the object approaches as time goes on. (b) For fixed t, use l'Hospital's Rule to calculate lim c→0+ v. What can you conclude about the velocity of a falling object in a vacuum? An object falling in a vacuum will accelerate at a slower rate than an object not in a vacuum. The velocity of a falling object is proportional to its mass in a vacuum. The velocity of a falling object in a vacuum is directly proportional to the amount of time it falls. The heavier the object is the faster it will fall in a vacuum.
