Well, the cat is already out of the bag on this one.

    As stated in Newton's 2nd Law, an applied force is what causes an object to accelerate. The force along with the mass of an object determines the degree of response (acceleration) that the object experiences as a result of the force. This is an important point that some people gloss over when they first learn physics.

    And, it is precisely the reason why I have written the mathematical formulation of Newton's 2nd Law as a = F/m instead of the more familiar F = ma. Nothing has changed by rewriting the formula. It was done purely for the sake of clarity. By writing it as a = F/m, we are emphasizing that it is force which causes an object to accelerate and not the other way around. Acceleration does not cause a force.

    Mass In the form, a = F/m, it is also easier to determine the effect of mass on the amount of acceleration that an object experiences as a result of an applied force. Since mass, m, appears on the bottom, we know that mass is inversely related to acceleration. What this means is that if the same amount of force is applied to two objects, the object with the larger mass will experience a smaller amount of acceleration (or response to the force). Remember the example on the previous page about pushing the cotton ball and the elephant with the same amount of force. The reason why this is apparent from the formula above is because we know that, if we divide by a larger number, the result will be a smaller quantity. Therefore, when you have a more massive object, you are, in effect, dividing by a larger number thus resulting in a smaller quantity, acceleration, in this case.

    Forces Are Additive Next, I want to come back to another point I made earlier, namely that forces add. For this discussion, I will just consider motion in one dimension. This fact is so obvious it almost needs no introduction, but, nevertheless, I'll provide an example to motivate the point. If you and a friend push a box with the same amount of force but in opposite directions, the box won't move (not a very good thing to do when moving things). This is because the forces add up. In this case, the forces cancel one another. Let me provide another obvious example to further illustrate the point. You already know that it is easier to push a stalled car when two people are pushing it instead of just one person. Well, this is obvious you might say, but it provides an example of the additive nature of forces. Let us assume that it takes 50 Newtons of force to move a stalled car. If you were just pushing it by yourself, you would have to provide all of this force by yourself. However, if two people are pushing the car, your combined total would have to be 50 Newtons. So, you could push 20 Newtons, and your friend could push 30 Newtons so that the total force would still be 50 Newtons. However, we know that this example is completely hypothetical because you would never let your friend push more Newtons than you.

    Direction Now that we know there is a relationship between force and acceleration, let me introduce another point that might sound obvious. As you already know, acceleration also involves a direction because the definition of acceleration involves velocity which has a direction associated with it. Likewise, force has a direction, namely the direction in which it is applied. So, it should come as no surprise that the direction in which the force is applied is also the direction in which the object accelerates. This should be obvious because the acceleration that an object experiences is the direct response to the applied force. The object should accelerate in the direction in which the force is applied. If it didn't, then it would seem weird. Recall that acceleration is the change in velocity over time. Therefore, a force causes an object to change its velocity. Remember Newton's 2nd Law. Objects naturally like to keep a constant velocity (zero velocity is just a special case of constant velocity) unless they are perturbed by a nonzero net (or total) force.

    Constant acceleration is an important special case where we can learn about the motion of an object without doing a lot of actual math. You might be tempted to say, "Hold it there, Tex." We just spent an entire section talking about how useful it is to think of force when we want to determine the direction of the acceleration. You might have even thought to yourself, "Why even bother with acceleration? What good is it for?"

    Well, the answer is that force can only tell us some general things about the motion of an object, like whether it will speed up or slow down, but it can't tell us the specifics, like by how much it will speed up or slow down. For that, we will need acceleration.

    Recall that acceleration is defined as the change in velocity over the change in time. In other words, acceleration tells us how an object moves by telling us how its velocity changes over time.