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.

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. thus, the charge can be considered to be distributed uniformly throughout the cloud. for the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. the point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. this breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. the ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. in addition, the large current will heat up the air, resulting in its rapid expansion. these two phenomena account for the appearance of lightning and the sound of thunder. take the breakdown electric field of air to be eb=3.00ă—106n/c. part a estimate the total charge q on the cloud when the breakdown of the surrounding air is reached. express your answer numerically, to three significant figures, using ďµ0=8.85ă—10â’12c2/(nâ‹…m2) .

In a system, when potential energy decreases, then entropy also decreases. true false

If two students are running down the hall toward each other, trying to get to class, and they have the same mass and acceleration, what will happen when they collide? will their forces cancel out or will each one experience a reaction?