Momentum and Acceleration

Momentum is defined as mass times velocity, acceleration is the rate of change of velocity.

To be more accurate, velocity is a vector quantity, it has both magnitude and direction. Momentum is therefore also a vector quantity in the direction of the velocity with magnitude equal to the mass times the magnitude of the velocity:

1) p = mv

Acceleration is also a vector quantity and in the direction of the change in velocity direction and represents the rate of change of velocity:

2) a = dv/dt

Force is defined as the rate of change of momentum, and is therefore also a vector in the direction of the momentum change:

3) F = dp/dt

Substituting 1) in 3) we get:

4) F = m(dv/dt)

And since 2) defines dv/dt as acceleration we get:

5) F = ma
Which, as you know, is one of Newton's laws.


From wikipedia
"When a force is applied to a rigid body it changes the momentum of that body. A small force applied for a long time can produce the same momentum change as a large force applied briefly, because it is the product of the force and the time for which it is applied that is important."

Impulse is force*time, basically.

The formula for force: F= ma
The formula for momentum: p=mv
The formula for impulse: I = delta(F) * time


So, you'd need to know the time.

You forgot the source.

Well, let's assume the crazy idea that Hazzy has: that all the momentum is transferred to the human, and that the cannon-ball has 0 momentum afterwards.

A simple answer would then be that the average acceleration is the difference in speed divided by the amount of time. The amount of time here is the amount of time the man and the cannon-ball touch eachother. But since we don't have that, that's the information we need. From what Stereo said, the reason they contact in more than an infinitesimal period of time is because of the compression (and expansion) of the man.

Of course, the average acceleration is not the constant acceleration at any given time t: You could approximate the constant acceleration by using this formula:



Where t = 0 is the start of the touch, and t = 2b is the end of the touch. k is a constant so that



(I don't think this is something you have to say, though.)

Noah