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

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Answer 1 · 2016-05-04T17:35:31

$v(7)=(16-sqrt2 pi)/8$

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

$v(t)=d/(d t)(2t-cos(pi/4t))$

$v(t)=2+pi/4sin(pi/4t)$

$v(7)=2+pi/4sin(pi/4*7)$

$v(7)=2+pi/4*(-sqrt2/2)$

$v(7)=2-(sqrt2pi)/8$

$v(7)=(16-sqrt2 pi)/8$

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