First, realize that the force that the lighter child exerts on heavier child is equal and opposite to the force the heavier child exerts on the lighter child, as per Newton's third law.

Using Newton's second law, we can re-write this equation.

The question tells us that , making  the heavier child and  the lighter child. We can use this in our equation as well.

We are looking for the ratio of  to , so we need to rearrange the equation.

First, the masses cancel out.

Then, divide both sides by .

The ratio of   to is .

The relationship between force and acceleration is .

Since the crate has a constant velocity, it has no acceleration.

If there is zero acceleration, that means there is no net force on the object, or .

Newton's second law states that . We know the mass, but we need to calculate the acceleration.

Acceleration is the change in velocity per unit time.

Since the velocity does not change from one moment to the next, then there must be no net acceleration on the object.

Returning to Newton's second law, we can see that if there is no acceleration, then there is no net force.

The equation for a force is:

We can write this equation in terms of each object:

We know that the force applied to each object will be equal, so we can set these equations equal to each other.

We know that the second object is twice the mass of the first.

We can cancel out the mass from each side, leaving a relationship between the two accelerations.

The acceleration on the first mass is twice the acceleration on the second; thus, the acceleration of the lighter mass is greater.

The formula for force is Newton's second law:

We are told in the question to use for the mass and for the force.

Now we can isolate the acceleration.

This also makes sense from a units perspective. Units for force are Newtons, which can be written as:

In our equation, we can see that Newtons are divided by mass:

This would result in the units for acceleration.

If there are no forces acting upon the object, then there is no acceleration. If there is no acceleration, then the object will move with a constant velocity.

Mathematically, we can look at Newton's second law and the formula for acceleration.

We know that the force is zero.

Since we know that the mass cannot be zero, the acceleration must be zero.

We can now use the formula for acceleration to see the effects on velocity.

We know that the acceleration is zero and that the time is ten seconds.

In order for this to be true, the initial and final velocities must be equal.

If the bone does not move, then we know that the resultant acceleration on it is zero. That means that the net force must also equal zero. 

In other words, the sum of the two forces acting on the bone must be zero.

Since the forces are pulling in opposite directions, one force must be in the negative direction.

From here, it's simple manipulation to see that the forces are equal.

The forces are equal in size, but going in opposite directions.

If no forces are acting upon the skater and he is on a frictionless surface, then that means he has no net acceleration.

Mathematically, we can see this relationship from Newton's second law:

Presumably the skier has mass, therefore the acceleration must be zero.

If an object moves with a velocity and there is no acceleration, then the velocity remains constant. His velocity after five second will be equal to his initial velocity.

There is insufficient information to solve. Force is the product of mass and acceleration. While we are given the mass, we are not given an acceleration.

If we assume that we are looking for the minimum force required to move the cabinet, then the force would be equal to the force of friction.

Substitute the equations for frictional force and Newton's second law.

Normal force is equal to the force of gravity.

The masses cancel out and we know the acceleration due to gravity is constant.

This equation is unsolvable as we do not know , the coefficient of friction between the cabinet and the floor. We cannot find the acceleration of the cabinet, meaning we cannot find the force.

Acceleration results from a change in velocity. Despite the speed remaining constant, velocity is a vector quantity and will change if the car changes direction. In rounding the turn, there is a change in the direction of the velocity, but not in the magnitude. This change in direction causes a non-zero acceleration.

The acceleration will remain equal to the equation for centripetal acceleration:

As long as the magnitude of the velocity and the radius of the turn do not change, the acceleration will remain constant.