# Why is force dependent on acceleration, not velocity?

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?

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force is a result of acceleration and mass, right? Wrong. The net force equals the time rate of change of momentum: $\vec F_{net} = \frac{d\vec p}{dt} = m\vec a$. Based on the way your question is phrased, I wonder if you're conflating the notion of impulse with force: en.wikipedia.org/wiki/Impulse_%28physics%29 –  Alfred Centauri Mar 18 '14 at 2:27
The only way to get force from an impact velocity is F = mv^2/d. Which works great, but only if you can figure out what the d is. No ideas? It is how long it takes for the two masses to exchange energy and momentum. Which is really hard to figure out ahead of time, and one good reason that this approach isn't used much. –  RBarryYoung Mar 18 '14 at 2:40

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.
@user2612743 To calculate the force in collisions you us the impulse divided by time, or $F_{net}=\Delta P/\Delta t$. –  Ruben Mar 19 '14 at 6:20