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

##### 1 Answer

#### Answer:

#### Explanation:

We're asked to find the magnitude and direction of an object's acceleration at a certain time given its velocity equation.

In component form, the velocity is

To find the acceleration as a function of time, we must **differentiate** the velocity equations:

At

(The term

The **magnitude** of the acceleration is

The **direction** is

*Always check the arctangent calculation to make sure your answer is not #180^"o"# off!*