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

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Answer 1 · 2016-05-17T06:22:50

$v(4)=1+pi$

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

$v(t)=d/(d t) (t-t sin(pi/4 t))$

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

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

$v(4)=1-(sin pi+pi*cos pi)$

$sin pi=0$
$cos pi=-1$

$v(4)=1-(0-pi)$

$v(4)=1+pi$

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