# An object is at rest at #(7 ,6 ,4 )# and constantly accelerates at a rate of #7/4 m/s^2# as it moves to point B. If point B is at #(5 ,1 ,7 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

The time is

Apply the equation of motion

Therefore,

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To calculate the time it takes for the object to reach point B, use the kinematic equation:

[d = ut + \frac{1}{2}at^2]

Where:

- (d) is the displacement (distance between points A and B)
- (u) is the initial velocity (assumed to be zero as the object is at rest)
- (a) is the acceleration
- (t) is the time

Rearrange the equation to solve for (t):

[t = \sqrt{\frac{2d}{a}}]

Substitute the values:

[d = \sqrt{(5-7)^2 + (1-6)^2 + (7-4)^2}] [a = \frac{7}{4}]

Calculate (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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