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

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Answer 1 · 2017-02-28T09:22:08

#"The speed of object at t=7 is v(7)=3.78"#

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

#(d p(t))/(d t)=3+pi/8*sin(pi/8 t)+0#

#v(t)=3+pi/8*sin(pi/8 t)#

#v(7)=3+pi/8+sin(pi/8*7)#

#sin((7pi)/8)=0.38268343#

#v(7)=3+pi/8+0.38268343#

#v(7)=pi/8+3.38268343#

#pi/8=0.39269908#

#v(7)=0.39269908+3.38268343=3.7753825#

#v(7)=3.78#