applied mathematics - unit 1: exam
a scientist places 4 cells in a petri dish. every hour, the cells divide in 2. how many cells are there after 9 hours?
2048
a falling rock produces a force of 250 newtons from acceleration due to gravity alone. what is the rock's mass in kilograms?
25.5 kg
a 60-kilogram person stands on a compression spring. the spring constant is 2500 newtons per meter. what is the displacement of the spring?
0.2352 m
what is the acceleration, in m/s^2, of a 2,000,000 -kilogram nasa rocket with an applied force of 20,000,000 newtons?
10
what force in newtons will accelerate a 7-kilogram bowling ball at 2.5 m/s^2?
17.5 n
there are 8.8 liters of gas in a piston at a pressure of 1.75 atmospheres. the temperature remains constant, and the gas is compressed to a volume of 6.2 liters. what is the new pressure, in atmospheres, inside the piston?
2.48
when a force of 36 newtons is applied to spring s1 and s2, the displacement of the springs is 6 centimeters and 9 cm, respectively. what is the difference between the spring constants of the two springs?
200
an object is launched straight up into the air with an initial velocity of 40 m/s, from a height 30 m above the ground. assuming that gravity pulls it down, changing its position by about 4.9 m/s^2, after how many seconds will the object hit the ground?
8.9
the isotope thulium-167 is used in laser scans for medical treatments. Its rate of decay is −0.075. how many days does it take 500 grams of the isotope to decay to 250 g?
9.2
the volume of gas in a container is 125,000 liters, and the pressure is 1.2 atmospheres. suppose the temperature remains constant, and the pressure changes to 1.6 atmospheres. what is the new volume of the gas in liters?
93750
which situation would best be modeled with a quadratic function?
a water balloon thrown up into the air
which terms describe the relationship between applied spring force and spring displacement? select all that apply.
linear directly proportional
the function h(t) = −16t^2 + 32^t + 24 represents the height of an object t seconds after being launched straight into the air. what does −16 represent?
acceleration due to gravity
which statement represents boyle's Law for a constant temperature?
decreasing volume of gas increases pressure exerted by the gas.
a parent pushes a single child on a swing. suppose two children now sit on the same swing, and the parent pushes with the same force. according to newton's second law of motion, what is the result?
mass increases, acceleration decreases
which situations are best modeled with exponential decay? select all that apply.
the deer population of a state decreases 0.25% each year. a scientist claims glaciers are losing 1% of their mass each year.
