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 #?

1 Answer
May 20, 2016

Answer:

#s = 3+(pi sqrt(3))/6 ~= 3.91#

Explanation:

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:

#s = | d/(dt)p(t)| = |dot p (t)|#

In our case we need to do the derivative of our function:

#dot p(t) = d/(dt)p(t) = 3 + pi/3 sin(pi/3 t)#

plugging in the time given

#dot p(2) = 3 + pi/3 sin(2pi/3) = 3+(pi sqrt(3))/6#

Therefore the speed, being the absolute value of this, is the same:

#s = 3+(pi sqrt(3))/6 ~= 3.91#