The position of an object moving along a line is given by #p(t) = 4t - tsin(( pi )/8t) #. What is the speed of the object at #t = 5 #?

1 Answer
Oct 14, 2016

Answer:

#v(5)=3.83#

Explanation:

#"derivate the function p(t)"#

#(d p(t))/(d t)=v#

#v:"represents speed of object"#

#v(t)=d/(d t)(4t-tsin(pi/8t))#

#v(t)=4-1*sin(pi/8*t)-t*pi/8*cos(pi/8*t)#

#v(5)=4-sin((5pi)/8)-(5pi)/8*cos((5pi)/8)#

#sin(5pi)/8=0.92#

#cos(5pi)/8=-0.38#

#v(5)=4-0.92+(5pi)/8*0.38#

#v(5)=3.08+0.75#

#v(5)=3.83#