An athlete leaves one end of a pool of length l at t 5 0 and arrives at the other end at time t1. she swims back and arrives at the starting position at time t2. if she is swimming initially in the positive x direction, determine her average velocities symbolically in (a) the first half of the swim, (b) the second half of the swim, and (c) the round

a) v = L / (t1 - t0)

b) v = - L / (t2 - t1)

c) v = 0

Explanation:

The average velocity is calculated using the following equation:

v = (final position - initial position) / (final time - initial time)

a) For the first half of the swim:

final position = L

initial position = 0

initial time = t0

final time = t1

Then, the velocity will be:

v = (L - 0) / (t1 - t0) = L / (t1 - t0)

b) For the second half of the swim:

Final position = 0

initial position = L

final time = t2

initial time = t1

The velocity will be:

v = (0 - L)/ (t2 - t1) = - L / (t2 - t1)

c) For the round:

Final position = L

Initial position = L

initial time = t0

final time = t2

Velocity:

v = (L - L)/( t2 - t0) = 0

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

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.