The position of an object moving along a line is given by $p(t) = 3t - tcos(( pi )/4t)$ . What is the speed of the object at $t = 5$ ?

Question

1397 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-15T09:20:15

$v(5)=0.931$

$"We need to find the time derivative of the function."$

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

$v(t)=d/(d t) (3t-t cos(pi/4 t)$

$"We get;"$

$v(t)=3-1*cos(pi/4 t)+t*pi/4sin(pi/4 t)$

$"for t=5"$

$v(5)=3-cos((5pi)/4)+5*pi/4 sin((5pi)/4)$

$cos((5pi)/4)=-sqrt2/2=-0.707$

$sin((5pi)/4)=-sqrt 2/2=-0.707$

$v(5)=3+0.707-5*pi/4*0.707$

$v(5)=3.707-(3.535*pi)/4$

$v(5)=3.707-2.776$

$v(5)=0.931$

The position of an object moving along a line is given by p(t) = 3t - tcos(( pi )/4t) p(t) = 3t - tcos(( pi )/4t) . What is the speed of the object at t = 5 t = 5 ?