# An object's two dimensional velocity is given by #v(t) = ( t^3, t-t^2sin(pi/8)t)#. What is the object's rate and direction of acceleration at #t=12 #?

##### 1 Answer

#### Explanation:

We're asked to find the magnitude and direction of the acceleration of an object at a certain time, given the velocity equations as functions of time.

To do this, we need to find the **acceleration** of the object as a suction of **differentiating** the velocity component equations.

We're given:

So

Now, we plug in

The **magnitude** of the acceleration is thus

(the *dimensional form* of the units for acceleration; I used it here since no units were given)

The **direction** is

**Always be sure to check your arctangent calculation, as it could be #180^"o"# off!**