The speed s of blood that is r centimeters from the center of an artery is given below, where c is a constant, r is the radius of the artery, and s is measured in centimeters per second. suppose a drug is administered and the artery begins to dilate at a rate of dr/dt. at a constant distance r, find the rate at which s changes with respect to t for c = 1.54 105, r = 1.3 10-2, and dr/dt = 1.0 10-5.

s = c(r^2 − r^2)

ds/dt =/s

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.