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

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Answer 1 · 2017-04-28T09:56:59

The speed is $=0.63ms^-1$

We need

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

The speed is the derivative of the position

$p(t)=2t-tsin(pi/8t)$

Therefore,

$v(t)=2-(sin(pi/8t)+t*pi/8cos(pi/8t))$

$=2-sin(pi/8t)-(tpi)/8cos(pi/8t)$

When $t=3$

$v(3)=2-sin(3/8pi)-(3/8pi)cos(3/8pi)$

$=2-0.92-0.45$

$=0.63ms^-1$

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