The position of an object moving along a line is given by #p(t) = 2t - tsin(( pi )/4t) #. What is the speed of the object at #t = 7 #?

1 Answer
Jun 3, 2016

Answer:

#v(7)=-1.117#

Explanation:

#p(t)=2t-t sin (pi/4 t)" the equation of object's position"#

#v(t)=d/(d t)p(t)=d/(d t) (2t-t sin(pi/4 t))#

#v(t)=2-[sin(pi/4 t)+t*pi/4 cos(pi/4t)]#

#v(7)=2-[sin(pi/4*7)+7*pi/4cos(pi/4*7)]#

#v(7)=2-[-0.707+7*pi/4 *0.707]#

#v(7)=2-[-0.707+3.887]#

#v(7)=2-3.117#

#v(7)=-1.117#