# An object's two dimensional velocity is given by v(t) = ( t-1/t, t^2). What is the object's rate and direction of acceleration at t=3 ?

Jan 13, 2017

The acceleration is =〈10/9,6〉 and the direction is $= 79.5$º

#### Explanation:

v=〈t-1/t,t^2〉

Acceleration is

a(t)=(dv)/dt=〈1+1/t^2,2t〉

Therefore,

a(3)=〈1+1/9,6〉=〈10/9,6〉

The direction is $= \arctan \left(\frac{6}{\frac{10}{9}}\right)$

$= \arctan \left(\frac{54}{10}\right) = 79.5$º