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

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Answer 1 · 2016-06-03T13:58:42

$v(7)=-1.117$

$p(t)=2t-t sin (pi/4 t)" the equation of object's position"$

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

$v(t)=2-[sin(pi/4 t)+t*pi/4 cos(pi/4t)]$

$v(7)=2-[sin(pi/4*7)+7*pi/4cos(pi/4*7)]$

$v(7)=2-[-0.707+7*pi/4 *0.707]$

$v(7)=2-[-0.707+3.887]$

$v(7)=2-3.117$

$v(7)=-1.117$

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