The position of an object moving along a line is given by #p(t) = 3t - cos(( pi )/3t) + 2 #. What is the speed of the object at #t = 2 #?
The speed of an object is the rate of change of it's position with respect to time - in other words, the magnitude of the derivative of the position with respect to time:
In our case we need to do the derivative of our function:
plugging in the time given
Therefore the speed, being the absolute value of this, is the same: