# An object is at rest at #(1 ,2 ,9 )# and constantly accelerates at a rate of #1 m/s^2# as it moves to point B. If point B is at #(3 ,1 ,4 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

We're dealing with one-dimensional motion with constant acceleration.

Let's look at our known quantities:

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To find the time it takes for the object to reach point B, use the formula:

[ \text{time} = \sqrt{\frac{2 \cdot \text{distance}}{\text{acceleration}}} ]

First, calculate the distance between the initial point and point B using the distance formula in three dimensions:

[ \text{distance} = \sqrt{(3 - 1)^2 + (1 - 2)^2 + (4 - 9)^2} ]

[ \text{distance} = \sqrt{2^2 + (-1)^2 + (-5)^2} ]

[ \text{distance} = \sqrt{4 + 1 + 25} ]

[ \text{distance} = \sqrt{30} ]

Now, plug the values into the time formula:

[ \text{time} = \sqrt{\frac{2 \cdot \sqrt{30}}{1}} ]

[ \text{time} = \sqrt{2 \cdot \sqrt{30}} ]

[ \text{time} \approx \sqrt{2} \times \sqrt{\sqrt{30}} ]

[ \text{time} \approx \sqrt[4]{60} ]

[ \text{time} \approx 2.89 , \text{s} ]

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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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