# An object is at rest at #(4 ,5 ,1 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(7 ,2 ,6 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

It takes

The equation of motion for a constant accelerating object is

We are interested in the time that is

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To find the time it takes for the object to reach point B, we first need to find the displacement vector from the initial position to point B. Then, we can use the kinematic equation (s = ut + \frac{1}{2}at^2) to find the time, where (s) is the displacement vector, (u) is the initial velocity (which is 0 since the object starts at rest), (a) is the acceleration, and (t) is the time.The displacement vector from (4, 5, 1) to (7, 2, 6) is (7-4, 2-5, 6-1) = (3, -3, 5).

The magnitude of this displacement vector is √(3² + (-3)² + 5²) = √(9 + 9 + 25) = √43.

Using the formula (s = ut + \frac{1}{2}at^2), where (s) is the magnitude of the displacement vector, (u) is the initial velocity (0 m/s), (a) is the acceleration (4/3 m/s²), and (t) is the time, we can solve for (t):

(\sqrt{43} = 0 \cdot t + \frac{1}{2} \cdot \frac{4}{3} \cdot t^2)

(\sqrt{43} = \frac{2}{3} t^2)

(t^2 = \frac{3}{2} \cdot \sqrt{43})

(t = \sqrt{\frac{3}{2} \cdot \sqrt{43}})

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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.

- An object is at rest at #(4 ,8 ,3 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(3 ,5 ,7 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
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- The position of an object moving along a line is given by #p(t) = sin(t- pi /4) +3 #. What is the speed of the object at #t = pi/4 #?
- What is the speed of an object that travels from #( 8 , 4, 5 ) # to #( 6 , -4, ,2 ) # over #4 s#?
- A projectile is shot from the ground at a velocity of #15 m/s# at an angle of #pi/6#. How long will it take for the projectile to land?

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