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 $t = 5$ ?

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Answer 1 · 2016-10-14T07:44:32

$v(5)=3.83$

$"derivate the function p(t)"$

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

$v:"represents speed of object"$

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

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

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

$sin(5pi)/8=0.92$

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

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

$v(5)=3.08+0.75$

$v(5)=3.83$

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