velocity v = \frac{change in position}{change in time} = \frac{displacement}{time interval}

average velocity = \frac{x_{2} − x_{1}}{t_{2} − t_{1}}

instantaneous velocity = lim_{(t_{2}−t_{1})→0} (\frac{x_{2} − x_{1}}{t_{2} − t_{1}} ) = \frac{dx}{dt}

acceleration a = \frac{change in velocity}{change in time}

v_{f} = 60 (\frac{miles}{hour}) × (\frac{1609 m}{1 mile}) × (\frac{1 hour}{3600 s}) = 26.8 \frac{m}{s} average acceleration a = \frac{26.8 m/s − 0 m/s}{4.8 s} = 5.6 \frac{m}{s^{2}}

instantaneous acceleration = lim_{(t_{2}−t_{1})→0} (\frac{v_{2} − v_{1}}{t_{2} − t_{1}} ) = \frac{dv}{dt} = \frac{d^{2}x}{dt^{2}}

y(t) = 10 m + (3 \frac{m}{s}) t − (4.9 \frac{m}{s^{2}}) t^{2}