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An object traverses a pipe with a velocity that obeys the following dependence on time, !...

An object traverses a pipe with a velocity that obeys the following dependence on time, ! v =αt 2 + βt , where the velocity is measured in m/s and the time, t, in seconds. α and β are constants, α = −5⋅107 ,β = 3⋅105 . The acceleration of the object just as it leaves the pipe is zero.

(a) What are the units of the constants α and β? Rewrite the velocity expression using the values of these constants and their appropriate units.

(b) Derive expressions for the acceleration and position of the object as a function of time when the object is in the pipe. Please make sure to include the appropriate units of the coefficients that show up in your derived expressions.

(c) Calculate the time it takes the object to cross the pipe, and its speed as it exits the pipe.

(d) Determine the length of the pipe.

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