# An object's velocity is given by #v(t) = (2t^2 +t +1 , sin2t )#. What is the object's rate and direction of acceleration at #t=6 #?

##### 1 Answer

#### Explanation:

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

To do this, we need too **differentiate** the velocity component equations, which are given as

Finding the derivatives:

*I'll assume this is in radians*)

Plugging in

(The *dimensional form* of the units for acceleration (

The **magnitude** of the acceleration is thus

And the **direction** is

**Always make sure your arctangent calculation is in the right direction; it could be #180^"o"# off!**