The position of an object moving along a line is given by p(t) = cos(t- pi /3) +1 . What is the speed of the object at t = (2pi) /4 ?

1 Answer
JMicheli
Jul 12, 2016

v((2pi)/4) = -1/2

Explanation:

Since the equation given for the position is known, we can determine an equation for the velocity of the object by differentiating the given equation:

v(t) = d/dt p(t) = -sin(t - pi/3)

plugging in the point at which we want to know speed:
v((2pi)/4) = -sin((2pi)/4 - pi/3) = -sin(pi/6) = -1/2

Technically, it might be stated that the speed of the object is, in fact, 1/2, since speed is a directionless magnitude, but I have chosen to leave the sign.

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