- #1

joshmccraney

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## Homework Statement

A piecewise-continuous function models the velocity of a train (fps) as follows:

$$

v(t) =

\begin{cases}

80, & \text{if }\text{t>15} \\

bt+ct^2+dt^3, & \text{if }t\text{ <15}

\end{cases}

$$

How much time does it take the train to travel 5280 ft?

## Homework Equations

$$(1) vdv=ads$$

$$(2) ds=vdt$$

$$(3) dv=adt$$

where s is distance, v is velocity, t is time, a is acceleration

## The Attempt at a Solution

i have: [itex]5280=80t+15^2b+15^3c+15^4d[/itex] by integrating the piecewise function and using [itex](2)[/itex]. it seems if i can find variables [itex]b,c,d[/itex] i will be done.

i have [itex]80=bt+ct^2+dt^3[/itex] from the continuity of the function (given)

by [itex](3)[/itex] i have [itex]0=b+2*15c+3*15^2d[/itex]

it seems if i can find one more equation for [itex]b,c,d[/itex] i'll be done. i don't think i can use [itex](1)[/itex] as i do not have velocity as a function of distance. ive used the other two equations, so i feel i am close. any help is very appreciated. Thanks!