There are two forces in play in this scenario. The first is gravity, and the second is air resistance. Since they are opposing each other, we can write:

Substituting in Newton's second law, we get:

Rearranging for the force of air resistance, we get:

Plugging in our values from the problem statement:

We can use the equation for conservation of energy to calculate the velocity of the diver as he hits the water:

Cancel out initial kinetic and final potential energies, and plug in our expressions:

Cancel out mass and rearranging for final velocity:

Plug in our values:

We know that the diver then decelerates from this velocity to zero in 0.8 seconds, so we can calculate the acceleration:

Then use Newton's second law to calculate the force on the diver:

The car and the truck experience equal and opposite forces, but since the car has a smaller mass it will experience greater acceleration than the truck according to the equation F = ma.

A greater mass will decrease the acceleration.

Since we are neglecting air resistance, there are two forces in play: gravity and friction. Therefore, we can use Newton's second law to write the following:

Substituting in an expression for the force of gravity and rearranging for the force of friction, we get:

Use Newton's second law.

The box has a constant force acting on it pulling it towards the left. Therefore we can write this as:

, where the negative sign indicates that the force is directed towards the left.

Since the force is constant, this means that is is causing the box to move with a constant acceleration that we can calculate using Newton's second law of motion:

Now that we know the acceleration, we can calculate the final velocity after 5 seconds:

Where  and  since the box is originally at rest.

So we have that

.

Note that the negative sign indicates that the box is moving to the left.

The force applied by the weaker person can be calculated using Newton's second law, which states: 

The net force is equal to the product of the mass of the object and the acceleration of the object. We were given the mass and acceleration of the object, but only the ratio of the applied forces:

Solve for , the applied force from the weaker person:

Newton's second law states that the net force, or the vector sum of all the forces acting on an object, equals the mass times the acceleration. So, it is possible to have forces act on an object without acceleration if the forces are oriented such that they vector sum to zero. An example would be a person sitting in a chair. Gravity and the normal force both act on the person. However, these forces are equal in magnitude and opposite in direction. So the person doesn't accelerate. 

Acceleration requires a change in one of two quantities: speed and direction

The elevator is traveling only upwards and at a non changing speed. The accleration is zero and thus the net force must be zero by newton's second law.

The bird taking flight is accelerating from rest to some non-zero speed. Net force is non zero because the speed changes. 

The child on the swing set changes direction due to traveling in a semi-circle. Also their speed will change as well. Net force is non zero because both the speed and direction change.

The car breaking to a stop is changing speed. Net force is non zero because the speed changes. 

The airplane, while maintaining a constant speed, changes direction and therefore accelerates. Net force is non zero because the direction changes.

For this, we have to know that:

, where  is a force,  is an object's mass, and  is its acceleration. 

The text tells us that the electrostatic force between the proton and electron will exert the same force, but that the mass of the proton is  times the mass of the electron. 

, where  is the force on the proton and  is the force on the electron. 

To determine the effect on their acceleration:

, where  and  are the masses of the proton and electron respectively, and  and  are the acceleration of the proton and electron respectively. 

Since we know that 

Solving for the acceleration of the proton:

The acceleration of the proton is  of the acceleration of the electron.