# 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 #?

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:

The magnitude of the acceleration is

The direction is

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The object's rate of acceleration at ( t = 2 ) is ( (2, -\sin(2)) ) and its direction of acceleration is ( \theta = \tan^{-1}\left(\frac{-\sin(2)}{2}\right) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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