The position of an object moving along a line is given by $p (t) = t - cos (\frac{π}{4} t)$ $p(t) = t-cos(( pi )/4t)$ . What is the speed of the object at $t = 7$ $t = 7$ ?

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Answer 1 · 2017-11-19T13:05:49

The speed is $= 0.44 m s^{- 1}$ $=0.44ms^-1$

The speed is the derivative of the position

$p (t) = t - cos (\frac{1}{4} π t)$ $p(t)=t-cos(1/4pit)$

$v(t)=p'(t)=1+1/4pisin(1/4pit)$

Therefore,

When $t=7s$

$v(7)=1+1/4pisin(1/4pixx7)=1+1/4pisin(7/4pi)$

$=0.44ms^-1$

The position of an object moving along a line is given by p(t) = t-cos(( pi )/4t) p(t)=t−cos(π4t)p(t) = t-cos(( pi )/4t) . What is the speed of the object at t = 7 t=7t = 7 ?