The position of an object moving along a line is given by $p(t) = sin(t- pi /4) +1$ . What is the speed of the object at $t = pi/3$ ?

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Answer 1 · 2017-05-02T21:07:55

The speed is $=0.97ms^-1$

The speed is the derivative of the position.

$p(t)=sin(t-pi/4)+1$

$v(t)=p'(t)=cos(t-pi/4)$

Therefore,

when $t=pi/3$

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

$=cos(pi/12)$

$=0.97ms^-1$

The position of an object moving along a line is given by p(t) = sin(t- pi /4) +1 p(t) = sin(t- pi /4) +1 . What is the speed of the object at t = pi/3 t = pi/3 ?