# The position of an object moving along a line is given by p(t) = t^3 - 2t +2. What is the speed of the object at t = 5 ?

Speed is the first derivative of position, $p ' \left(t\right) = 3 {t}^{2} - 2$. Substituting in $t = 5$ $s$ yields $s p e e d = p ' \left(t\right) = 3 {\left(5\right)}^{2} - 2 = 75 - 2 = 73$ $m {s}^{-} 1$.