The position of an object moving along a line is given by #p(t) = 7t - cos(( pi )/3t) + 2 #. What is the speed of the object at #t = 8 #?

1 Answer
Jan 23, 2017

Answer:

#7.907 m/s#

Explanation:

Speed is the magnitude of velocity. Velocity is the change in position. #p'(t)=v(t)#

#p(t)=7t-cos(pi/3t)+2 => p'(t)=v(t)=7+pi/3sin(pi/3t)#

at #t=8# we have #v(8)=7+pi/3sin(pi/3(8))=7+pi/3sin((2pi)/3)=7+pi/3(sqrt(3)/2)=7+(sqrt(3)pi)/6approx7.907m/s#