## Momentum & impulse

Momentum is a quantity of motion defined by

vec p = m vec v,

measured in kilogram-metres per second (kg·m/s). A change in momentum is called impulse, and it is defined by

Delta vec p = mDelta vec v = vec FDelta t.

A lightweight, fast-moving object can have the same momentum as a heavy, slow-moving object because mass and velocity are multiplied. Similarly, a large force applied over a short time interval can deliver the same impulse as a small force applied over a long time interval.

Just as the area under an acceleration-time graph represents Delta vec v, so too the area under a force-time graph represents Delta vec p.

### Example

What average force is needed to stop a 34 kg ball in 2.5 s if the initial speed of the ball is 19 m/s [fwd]?

Since vec FDelta t = mDelta vec v,

vec F = (mDelta vec v)/(Delta t) = (vec v_2 - vec v_1)/(Delta t) = ((34\ "kg")(0 - 19\ "m/s"))/(2.5\ "s") = -258.4\ "N",

therefore an average force of 260 N [bwd] is required.