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Math Help - Differentiation of trig functions sin and cos

  1. #1
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    Differentiation of trig functions sin and cos

    1 A particle is moving along a straight line so that, at a time t seconds after leaving a fixed point O, its velocity v ms-1 is given by V = 10sin t.
    a) Find the time when the acceleration, given by dv/dt , is first zero.
    b) Find the velocity at this instant.
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  2. #2
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    You're given the velocity function, so taking the derivative will give you the acceleration as a function of time.

    The derivative of the sin(x) function is cos(x), but you must remember to apply the chain rule fur the inside function in this case.

    Thus V' = acceleration = 10cos(t/2)*(1/2) = 5cos(t/2).

    Then find the points where acceleration is equal to zero and solve for t. You can then plug in the appropriate value of t into the velocity function for part b.
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