The position of an object moving along a line is given by $p(t) = cos(t- pi /3) +1$ . What is the speed of the object at $t = (2pi) /3$ ?

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Answer 1 · 2018-03-16T16:38:22

The speed is $=-sqrt3/2ms^-1$

The speed is the derivative of the position

$p(t)=cos(t-pi/3)+1$

$v(t)=p'(t)=-sin(t-pi/3)$

When $t=2/3pi$

$v(2/3pi)=-sin(t-pi/3)=-sin(2/3pi-pi/3)$

$=-sin(1/3pi)$

$=-sqrt3/2ms^-1$

The position of an object moving along a line is given by p(t) = cos(t- pi /3) +1 p(t) = cos(t- pi /3) +1 . What is the speed of the object at t = (2pi) /3 t = (2pi) /3 ?