In word form, Newton’s second law of motion is simplified to:

“The rate of change of momentum of a body is proportional to the imposed force and is in the direction of the force.”

Momentum as we all know is a vector quantity defined as the mass of a body multiplied by its velocity. Therefore, momentum is also a vector quantity.

So, in general terms, if we consider a body of mass (m) moving at velocity (v), its momentum (p) is given by:  P=mv

It is important to remember that momentum is a VECTOR quantity – so it has DIRECTION as well as MAGNITUDE.  Hence a change in momentum Δp = Δm x Δv.  Where Δm is any change in mass and Δv is any change in velocity.  It is the velocity (v) which is the corresponding VECTOR quantity on the right hand side of the P=mv equation.

Hence, Δv may mean a change in magnitude, eg, from 20 m/s to 15 m/s or a change in direction such as to the north from the north-east… OR even both!

The rate of change of momentum over a time period Δt is given by:

Δp/Δt = Δm x Δv/Δt.  Note that Δv/Δt is the rate of change of velocity – which is called acceleration “a” (another vector).  Also the impulse over the time period Δt which changes the momentum by Δp is actually the applpied force.  Therefore:

Δp/Δt  =  F,   and   (assuming no change in mass) we end up with…

F=ma