Question 1180995
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The distance traveled as a function of time is given by *[tex \Large s(t)\ =\ \frac{1}{2}at^2\ +\ v_ot\ +\ s_o].  Since, for this problem, the initial velocity is zero and the initial distance traveled is zero, this reduces to *[tex \Large s(t)\ =\ \frac{1}{2}at^2].  From the given information, we know this to be equal to 75 meters.


The velocity as a function of time is given by *[tex \Large v(t)\ =\ at\ +\ v_o].  Since the initial velocity is zero for this problem this reduces to *[tex \Large v(t)\ =\ at].  From the given information we know this to be equal to 25 meters per second.


Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ at^2\ =\ 150]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ at\ =\ 25]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{150}{25}\ =\ 6]


So the elapsed time at the point the distance was 75 meters and the velocity was 25 meters per second is 6 seconds.  Since 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ v(6)\ =\ 6a\ =\ 25]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ \frac{25}{6}\,\text{\frac{m}{sec^2}}]

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

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