The position of an object moving along a line is given by #p(t) = 3t - tcos(( pi )/4t) #. What is the speed of the object at #t = 7 #?

1 Answer
Nov 29, 2017

Answer:

#3 -sqrt(2)/2 - (7sqrt(2)pi)/8#

Explanation:

You're looking for the velocity of the object. You can find the velocity #v(t)# like this:
#v(t) = p'(t)#
Basically, we have to find #v(7)# or #p'(7)#.
Finding the derivative of #p(t)#, we have:
#p'(t) = v(t) = 3 - cos(pi/4t) + pi/4tsin(pi/4t)# (if you don't know how I did this, I used power rule and product rule)
Now that we know #v(t) = 3 - cos(pi/4t) + pi/4tsin(pi/4t)#, let's find #v(7)#.
#v(7) = 3 - cos(pi/4 * 7) + pi/4 * 7sin(pi/4 * 7)#
#=3 - cos((7pi)/4) + (7pi)/4 * sin((7pi)/4)#
#=3 - sqrt(2)/2 - (7pi)/4 * sqrt(2)/2#
#v(7) =3 -sqrt(2)/2 - (7sqrt(2)pi)/8#