A 5.25-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the end of the rope, and the height of the crate above its initial position is given by y(t).

Explanation:

The upward force of F(t) is applied at the free end . Therefore the acceleration of  mass , suspended from rope can be calculated as

The displacement S = u t + 1/2 a t²

By substituting the values  S = 0 + 1/2 x F(t)/5.25 x t²

or  y(t) = 1/2 x F(t)/5.25 x t²

Here u is the initial velocity , because mass was at rest in the beginning , hence it is zero .

The acceleration a = force/mass = F(t)/5.25

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

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.