The position of an object moving along a line is given by #p(t) = 3t - 2sin(( pi )/8t) + 2 #. What is the speed of the object at #t = 24 #?

1 Answer
Sep 3, 2016

Answer:

#v# = #3.785# #m/s#

Explanation:

The first time derivative of a position of an object gives the velocity of the object
#dot p(t) = v(t)#
So, to get the velocity of the object we differentiate the position with respect to #t#
#p(t)=3t-2sin(pi/8t)+2#
#dot p(t)=3-2*pi/8*cos(pi/8t)=v(t)#
So speed at #t=24# is
#v(t)=3-pi/4cos(pi/8*24)# ;or
#v(t)=3-pi/4(-1)# ;or
#v(t)=3+pi/4=3.785# #m/s#
Hence the speed of the object at #t=24# is #3.785# #m/s#