# An object's two dimensional velocity is given by #v(t) = ( t-2t^3 , 4t^2-3t)#. What is the object's rate and direction of acceleration at #t=3 #?

##### 1 Answer

The acceleration is the first derivative of the velocity,

which, evaluated at t=3 in standard form is

#### Explanation:

Taking the first derivative of the velocity, we get

Evaluating this at

The magnitude of this acceleration is found by Pythagorus' theorem because the two components above are perpendicular:

The direction is found from

But this angle cannot be right, because it would describe an acceleration vector pointing into quadrant 4 - with positive

So, you must be careful in how you interpret this last result. If you did the

A diagram will sort out the problem. With a negative

Always include a diagram when solving two-dimensional vector problems. It will help you avoid errors in calculation.