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24 February, 23:37

An automobile starts from rest and travels down a straight section of road. The distance s (in feet) of the car from the starting position after t seconds is given by s (t) = 5t3 (a) Find the instantaneous velocity (in feet per second) at t=4 seconds.

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  1. 24 February, 23:50
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    Answer: 240 ft/sec

    Explanation:

    If the distance s, of the car regarding his starting position, is defined as a function of time, by definition, the instantaneous velocity at any time, is given by the derivative of the displacement (distance from origin) respect the time, as follows;

    v = ds / dt ⇒ v = d/dt (5 t³) = 15 t² = 15 t²

    Replacing by t=4 s, we get:

    v = 15. 4² = 15.16 = 240 ft/sec
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