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

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Answer 1 · 2018-02-22T14:07:12

The speed is $=1.74ms^-1$

Reminder :

The derivative of a product

$(uv)'=u'v-uv'$

$(tsin(pi/8t))'=1*sin(pi/8t)+pi/8tcos(pi/8t)$

The position of the object is

$p(t)=3t-tsin(pi/8t)$

The speed of the object is the derivative of the position

$v(t)=p'(t)=3-sin(pi/8t)-pi/8tcos(pi/8t)$

When $t=2$

$v(2)=3-sin(pi/4)-pi/4cos(pi/4)$

$=3-sqrt2/2-sqrt2/8pi$

$=1.74ms^-1$

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