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

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Answer 1 · 2017-12-11T11:16:56

The speed is $=1ms^-1$

The speed is the derivative of the position.

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

$v(t)=p'(t)=1+pi/2sin(pi/2t)$

Therefore, when $t=2$

$v(2)=1+pi/2sin(pi/2*2)$

$=1+pi/2sin(pi)$

$=1-0$

$=1ms^-1$

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