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.

Force is given by the product of mass and acceleration. If an object has a constant velocity, then it has no acceleration.

If an object has no acceleration, then it must also have no net force.

No additional information is needed to solve this question.

Since the object is moving with a constant velocity, it has no acceleration. Acceleration is only produced by a change in the velocity.

If acceleration is zero, no force is produced. This conclusion comes from Newton's second law:

Since the acceleration is zero:

Newton's second law states that:

We are told that the force on the object remains constant, even after it breaks in half. The mass of the broken piece will be equal to half the mass of the total object.

Using these values, we can set up equations for the initial and final accelerations.

If the force remains constant while the mass is cut in half, the acceleration of the object will double. The ratio of the new acceleration to the old acceleration will be 2:1. If the question asked for the ratio of the old acceleration to the new one, it would be 1:2.