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

Nov 19, 2017

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

#### Explanation:

The speed is the derivative of the position

$p \left(t\right) = t - \cos \left(\frac{1}{4} \pi t\right)$

$v \left(t\right) = p ' \left(t\right) = 1 + \frac{1}{4} \pi \sin \left(\frac{1}{4} \pi t\right)$

Therefore,

When $t = 7 s$

$v \left(7\right) = 1 + \frac{1}{4} \pi \sin \left(\frac{1}{4} \pi \times 7\right) = 1 + \frac{1}{4} \pi \sin \left(\frac{7}{4} \pi\right)$

$= 0.44 m {s}^{-} 1$