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

##### 1 Answer

Jan 30, 2017

#### Answer:

We take the first derivative with respect to time to get the component (rectangular) form of the acceleration, then change this to standard (polar) form, to get the acceleration as

in a direction of 36.9° south of east.

#### Explanation:

Since the acceleration is the first derivative with respect to time, the acceleration must be

#a(t) = (6t-2, -3)

and at time

To change to standard form, we use the following operations:

The direction is given by

So, the acceleration is