# Defining Force

## Key Questions

• No, force is a vector quantity, it is defined by its magnitude and direction.

Common vector quantities are displacement, velocity, acceleration and force.

Common scalar quantities are distance, speed, work and energy.

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• Put simply, a force is something which changes the momentum of an object. The magnitude of a force is the rate of change of momentum caused.

This is shown by manipulation of the famous equation $F = m a$

$F = m a = m \frac{{v}_{f} - {v}_{i}}{t} = \frac{{p}_{f} - {p}_{i}}{t}$

Where $F$ is the force
$m$ is the mass of the object
$a$ is acceleration, which is the rate of change of velocity
${v}_{i}$ is the initial velocity of the object which the force acts upon
${v}_{f}$ is the object's final velocity
$t$ is time
$p$ is momentum, which is equal to $m \times v$

Extra info:
Of course, because force is the rate of change of momentum, it can be linked to an object whose mass changes while velocity remains constant.

$F = \frac{{p}_{f} - {p}_{i}}{t} = v \frac{{m}_{f} - {m}_{i}}{t}$

Where ${m}_{f}$ is final mass and ${m}_{i}$ is initial mass.

Force can also be related to an object whose mass and velocity change simultaneously, but those equations involve calculus, so I won't include those here.