An object is at rest at #(5 ,2 ,1 )# and constantly accelerates at a rate of #2/3 m/s# as it moves to point B. If point B is at #(4 ,9 ,8 )#, 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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Using the kinematic equation ( \Delta x = v_i t + \frac{1}{2} a t^2 ), where ( \Delta x ) is the displacement, ( v_i ) is the initial velocity, ( a ) is the acceleration, and ( t ) is the time, we can solve for ( t ). Since the object starts from rest, ( v_i = 0 ). So, ( \Delta x = \frac{1}{2} a t^2 ). Given the coordinates, the displacement ( \Delta x ) is the change in position along the x-axis, which is ( 5 - 4 = 1 ) meter. Substituting the values, we have ( 1 = \frac{1}{2} \left(\frac{2}{3}\right) t^2 ). Solving for ( t ), we get ( t = \sqrt{\frac{3}{2}} ) seconds.
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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.
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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