The position of an object moving along a line is given by $p(t) = 7t - cos(( pi )/3t) + 2$ . What is the speed of the object at $t = 8$ ?

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Answer 1 · 2017-01-23T02:17:51

$7.907 m/s$

Speed is the magnitude of velocity. Velocity is the change in position. $p'(t)=v(t)$

$p(t)=7t-cos(pi/3t)+2 => p'(t)=v(t)=7+pi/3sin(pi/3t)$

at $t=8$ we have $v(8)=7+pi/3sin(pi/3(8))=7+pi/3sin((2pi)/3)=7+pi/3(sqrt(3)/2)=7+(sqrt(3)pi)/6approx7.907m/s$

The position of an object moving along a line is given by p(t) = 7t - cos(( pi )/3t) + 2 p(t) = 7t - cos(( pi )/3t) + 2 . What is the speed of the object at t = 8 t = 8 ?