accelerationnewtonian-mechanics
According to $F = ma$, force is a result of acceleration and mass, right?
However, I don't understand why velocity is not used instead of acceleration. A train moving at 100 miles/hour will still impart a great force on you even though it has no acceleration. Further, dropping a book at 10ft will impart a greater force on the gorund than dropping it at 1ft. So it seems that velocity would influence the force more than the acceleration would.
Why is this not the case?
Mark I liked his approach very much, by he stating his reasoning I had enough information to figure out where the flaws on his rationale were. Which for he to do it by himself would be much more difficult. The things I did not like in his question were, the vague title question, and that two question were asked in a single thread. fprime, to set an example, would split te two questions and reformulate it. I will put the proper answer after.
The second question you could have asked more directly.
Does the magnitude of the velocity of an object must change if the magnitude of its acceleration is a constant?
Then put your answer and rationale below.
Now lets go for the answers.
The definition you are working with is probably. "Acceleration is the rate by which the magnitude of the velocity changes". While the formal definition of acceleration is "Acceleration is the rate by which the velocity is changes". Now because velocity has the direction property it can change its direction without changing its magnitude. Changing direction IS a change in velocity.
We actually use the wrong definition all around in our daily life. When we say do not accelerate while turning in a curve. We mean do not step the gas. But by the formal definition, it is impossible to turn without accelerating. So when we hear this phrase we know the person is not using the formal acceleration concept.
So you must understand that in the question the formal definition is to be assumed. For it is this definition that is used in professional setting. So take care with it, all physics and engineering books and articles assume this the formal definition of acceleration.
You're confusing the acceleration of your car with the acceleration in a collision. You actually have to look at it "backwards" from what you've described above.
That is, in the collision you don't do a $F = ma$ calculation where $a$ is the acceleration of your gas pedal. Instead in the collision you have a force $F$ resulting from the collision and you do $a = F/m$ to get the resulting acceleration your car is subjected to.
Best Answer
The $F$ in the equation $F=ma$ is not the force that would be exerted by the object if it were to hit something else. Instead, $F$ represents the net force acting on the object that must be present in order to produce the current acceleration $a$ of the object. A better way to write Newton's second law is $$F_\text{net}=ma,$$ since it shows explicitly which force is being represented on LHS of the equation is.
In your train example, if the train is traveling at a constant velocity of 100 mph, the acceleration is zero, and by Newton's second law the net force is also zero. But this has no bearing on what force the train would exert on something if it collided.