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1. Position, Velocity, and Acceleration

• Position Function: The position function, denoted by $ s(t) $ , describes the location of an object at a given time $ t $ .

$$ s(t) = \text{The position of an object at time }t \text{ on a single axis} $$ * Velocity Function: The velocity function, denoted by $ v(t) $ , represents the rate of change of the object’s position with respect to time. Mathematically:

$$ v(t) = \frac{ds(t)}{dt} $$ Since velocity is speed and direction, and the sign is a direction( $ + $ or $ - $ ), the absolute value is the speed of the object

$$ Speed = |v(t)| $$

• Acceleration Function: The acceleration function, denoted by $ a(t) $ , represents the rate of change of the object’s velocity with respect to time. Mathematically:

$$ a(t) = \frac{dv(t)}{dt} = \frac{d^2s(t)}{dt^2} $$