Answer:
14.3
Explanation:
The distance s as a function of time can be written as:
[tex]s(t) = \sqrt{156^{2} + (31t)^2}[/tex]
The rate of change is the derivative of d with respect to time:
[tex]\frac{ds}{dt} =\frac{961t}{\sqrt{156^{2}+(31t)^{2}}}[/tex]
The time t when the track has been traveling for 81 miles is given by:
[tex]81 = 31t\\ t = \frac{81}{31}[/tex]
Using t in the previous equation gives:
[tex]\frac{ds}{dt}(\frac{81}{31} ) =\frac{2511}{\sqrt{156^{2}+81^{2}}}=14.3[/tex]
