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
Jul 12, 2016


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


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.