Ben rides a unicycle back and forth along a straight east-west track. The twice-differentiable function $B$ models Ben's position on the track, measured in meters from the western end of the track, at time $t$, measured in seconds from the start of the ride. The table above gives values for $B ( t )$ and Ben's velocity, $v ( t )$, measured in meters per second, at selected times $t$.
(a) Use the data in the table to approximate Ben's acceleration at time $t = 5$ seconds. Indicate units of measure.
(b) Using correct units, interpret the meaning of $\int _ { 0 } ^ { 60 } | v ( t ) | d t$ in the context of this problem. Approximate $\int _ { 0 } ^ { 60 } | v ( t ) | d t$ using a left Riemann sum with the subintervals indicated by the data in the table.
(c) For $40 \leq t \leq 60$, must there be a time $t$ when Ben's velocity is 2 meters per second? Justify your answer.
(d) A light is directly above the western end of the track. Ben rides so that at time $t$, the distance $L ( t )$ between Ben and the light satisfies $( L ( t ) ) ^ { 2 } = 12 ^ { 2 } + ( B ( t ) ) ^ { 2 }$. At what rate is the distance between Ben and the light changing at time $t = 40$ ?