# How many values of t does the particle change direction if a particle moves with acceleration #a(t)=3t^2-2t# and it's initial velocity is 0?

The particle changes direction for one value of t:

Since the initial velocity is 0 (when t=0):

Final Answer

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The particle changes direction when its velocity changes sign. To find where this occurs, we need to find the roots of the velocity function, which is the integral of the acceleration function. So, integrate (a(t) = 3t^2 - 2t) to get the velocity function (v(t)). Then, find the roots of (v(t)).

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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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