Question

Question #b1ade

Answer 1

`F=m * a`

Explanation:

`"Force" = "mass" xx "acceleration"`

Rate of change of momentum is directly proportional to force.
Change in momentum can be

`m * v_2 - m * v_1 = m * Deltav`, where `v_2` and `v_1` are different velocities.

Rate of change of momentum is

`d/(dt)(mv) = m * (dv)/(dt)`

But `(dv)/(dt)` is acceleration, so

`F = m * a`

Answer 2

`vec(F)=mvec(a)`

Explanation:

Newton's he second law of motion describes how the motion of an object behaves under the influence of an external force. Here `vec(F)` is the total force on an object, this is a vector, since it has both a direction and a magnitude, `m` the mass of the object and `vec(a)` the acceleration of the object, which is also a vector.

The law can also be written in a couple of different ways. since the acceleration is the change in velocity, and velocity the change in place, we can write `vec(a)=d/dtvec(v)=d/dtd/dtvec(x)=d^2/dt^2vec(x)`.
This means `vec(F)=md/dtvec(v)=d^2/dt^2vec(x)`.

Since the total mass of an object is usually constant, we can pull `m` through the derivation, meaning `vec(F)=(d(mvec(v)))/dt`. Since we have the momentum of an object `vec(p)=mvec(v)`, we can state
`vec(F)=(dvec(p))/dt`.
This can be used to show that in an isolated system the total momentum of all objects is conserved, which is an important result in classical physics.