The position of an object moving along a line is given by #p(t) = 4t - sin(( pi )/4t) #. What is the speed of the object at #t = 1 #?

1 Answer
Sep 27, 2017

Answer:

#4-pi/(4sqrt2)#

Explanation:

Position of an object #p(t)=4t-sin(pi/4t)#

Speed is defined as the rate of change in position of object with respect to time.
To find the speed we need to differentiate #p(t)# with respect to #t#.
speed #=d/dt(p(t))#
#v=d/dt(p(t))=d/dt(4t-sin(pi/4t))#
#v=4-(pi/4)cos(pi/4t)#

At time #t=1#
#v_(t=1)=4-(pi/4)cos(pi/4(1))=4-pi/4(1/sqrt2)=4-pi/(4sqrt2)#