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. 

In this question, we're being told that an object of a given mass is being subjected to a force. To solve this problem, we'll need to make use of Newton's second law, which states that an object of a given mass will accelerate at a rate that is proportional to the force that is applied. Or, written in equation form:

Plugging in the values given, we obtain:

Force is given by:

, where  is mass and  is acceleration. 

We're given mass, but we aren't given acceleration. Since the question asks for average force , we can determine average acceleration . 

, where  is the change in velocity and  is change in time. 

In our problem,  and 

Here we must use the following formula:

We can substitute our known values of mass and force and solve for acceleration

Since we know the acceleration and the time it acts upon the object, we can determine the final velocity through the following equation:

If the block is to remain at rest on the plane, we know that the sum of the forces acting a long the plane must be equal and opposite. This means that the gravitational force acting along the plane is equal to and opposite of the force of friction. This can be demonstrated as:

This can be rewritten as:

For the block to remain at rest, the force of static friction must exceed (for this problem we will set them equal to each other since it gives us the best approximation); solve for the angle:

Newton's second law states:

Where  is the net force exerted upon an object,  is the mass of the object and  is the acceleration of the object.

We rearrange this equation to show:

Plug in our given values with  and :

By Newton's second law:

, where  is force,  is mass, and  is acceleration.

This is the acceleration. Since we're assuming this acceleration is constant over time, we can model velocity  as: 

 where  is the initial velocity. 

Since the initial velocity is  in our problem, 

After  seconds, 

Use work:

All energy will be kinetic.

Convert  to :

Plug in values. Force will be negative as it is pointing against the direction of travel:

Solve for :

Use Newton's second law:

Plug in values:

Solve for :

Convert to

Use work:

All energy will be kinetic.

Convert  to :

Plug in values. Force will be negative as it is pointing against the direction of travel:

Solve for :

Use frictional force:

Plug in values:

Solve for