Rates Of Change

Suppose that an object is tossed directly upward in the air in such a way that the elevation of the object (measured in ft) is given by the function $\fe{s}{t}=150+60t-16t^2$ where $t$ is the amount of time that has passed since the object was tossed (measure in seconds).

Use the difference quotient to determine the average velocity of the object over the interval $\cinterval{4}{4.2}$ and then verify the value by calculating $\frac{\fe{s}{4.2}-\fe{s}{4}}{4.2-4}$.

Several applied functions are given below. In each case, find the indicated quantity (including unit) and interpret the value in the context of the application.

The velocity, $v$, of a roller coaster (in ft/s) is given by where $t$ is the amount of time (s) that has passed since the coaster topped the first hill. Find and interpret $\frac{\fe{v}{7.5}-\fe{v}{0}}{7.5-0}$.

Several applied functions are given below. In each case, find the indicated quantity (including unit) and interpret the value in the context of the application.

The elevation of a ping pong ball relative to the table top (in m) is given by the function $\fe{h}{t}=1.1\abs{\fe{\cos}{\frac{2\pi t}{3}}}$ where $t$ is the amount of time (s) that has passed since the ball went into play. Find and interpret $\frac{\fe{h}{3}-\fe{h}{1.5}}{3-1.5}$.

Several applied functions are given below. In each case, find the indicated quantity (including unit) and interpret the value in the context of the application.

The period of a pendulum (s) is given by $\fe{P}{x}=\frac{6}{x+1}$ where $x$ is the number of swings the pendulum has made. Find and interpret $\frac{\fe{P}{29}-\fe{P}{1}}{29-1}$.

Several applied functions are given below. In each case, find the indicated quantity (including unit) and interpret the value in the context of the application.

The acceleration of a rocket (mph/s) is given by $\fe{a}{t}=0.02+0.13t$ where $t$ is the amount of time (s) that has passed since lift-off. Find and interpret $\frac{\fe{a}{120}-\fe{a}{60}}{120-60}$.