# An object's two dimensional velocity is given by #v(t) = ( sqrt(t-2)-t , t^2-5t)#. What is the object's rate and direction of acceleration at #t=3 #?

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To find acceleration, differentiate velocity with respect to time:

a(t) = (1/(2√(t-2)) - 1, 2t - 5)

At t=3:

a(3) = (-1/2, 1)

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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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