The position of an object moving along a line is given by $p(t) = 2t - cos(( pi )/6t)$ . What is the speed of the object at $t = 3$ ?

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Answer 1 · 2018-04-05T05:13:16

The speed is $=2.52ms^-1$

The speed is the derivative of the position

$p(t)=2t-cos(pi/6t)$

$v(t)=p'(t)=2+pi/6sin(pi/6t)$

And when $t=3$

$v(3)=2+pi/6sin(pi/6*3)$

$=2+pi/6sin(pi/2)$

$=2+pi/6$

$=2.52ms^-1$

The position of an object moving along a line is given by p(t) = 2t - cos(( pi )/6t) p(t) = 2t - cos(( pi )/6t) . What is the speed of the object at t = 3 t = 3 ?