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.

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

Which of the following is the phase that results when the moon is on the opposite side of the earth from the sun? a. quarter moon b. crescent moon c. new moon d. full moon

Which best term to describe a chemical reaction that absorbs energy from its surroundings? a.thermal conductor b.thermal insulator c.endothermic d.exothermic