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    Derivatives : Displacement, Velocity and Acceleration

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    A car brakes in an emergency, the moment the brakes are first applied is t=0. the car's distance, s, from the point at which the brakes were first applied is given by:

    S = -0.1t^3 + 20t + 0.1

    (i) Differentiate s to find formulae for the velocity and acceleration.
    (ii) Find the time at which the car comes to a stop.
    (iii) How far does the car travels before it comes to a stop.
    (iv) What does the mathematical model say will happen to the car after it comes to a stop? What will actually happen? Why are the two different?

    Please see the attached file for the fully formatted problems.

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    https://brainmass.com/physics/velocity/derivatives-displacement-velocity-acceleration-231792

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    Hi there :)

    Here is your solution (i've assumed the units are seconds and metres as they're not in the question, so if you know different please alter them) ...

    Solution Summary

    A car brakes in an emergency, the moment the brakes are first applied is t=0. the car's distance, s, from the point at which the brakes were first applied is given by:

    S = -0.1t^3 + 20t + 0.1

    A range of questions are solved related to this function (see below)
    All solutions are provided with workings.

    $2.19