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

The time is

We utilize the equation of motion.

thus,

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Use the kinematic equation: ( \Delta x = v_0 t + \frac{1}{2} a t^2 ) where ( \Delta x ) is the displacement, ( v_0 ) is the initial velocity, ( a ) is the acceleration, and ( t ) is time.

Given: Initial position (( x_0, y_0, z_0 )) = (1, 3, 5) Final position (( x, y, z )) = (3, 6, 4) Acceleration (( a )) = 4/3 m/s²

Calculate displacement: (\Delta x = x - x_0), (\Delta y = y - y_0), (\Delta z = z - z_0)

Use the displacement values in the kinematic equation to solve for time (( 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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