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 = 5 #?

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Answer 1 · 2017-03-15T09:20:15

#v(5)=0.931#

#"We need to find the time derivative of the function."#

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

#v(t)=d/(d t) (3t-t cos(pi/4 t)#

#"We get;"#

#v(t)=3-1*cos(pi/4 t)+t*pi/4sin(pi/4 t)#

#"for t=5"#

#v(5)=3-cos((5pi)/4)+5*pi/4 sin((5pi)/4)#

#cos((5pi)/4)=-sqrt2/2=-0.707#

# sin((5pi)/4)=-sqrt 2/2=-0.707#

#v(5)=3+0.707-5*pi/4*0.707#

#v(5)=3.707-(3.535*pi)/4#

#v(5)=3.707-2.776#

#v(5)=0.931#