An object is at rest at #(6 ,5 ,9 )# and constantly accelerates at a rate of #4/3 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.
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To find the time it takes for the object to reach point B, we can use the kinematic equation:
[ \Delta x = v_i t + \frac{1}{2} a t^2 ]
Where:
- ( \Delta x ) is the displacement (change in position)
- ( v_i ) is the initial velocity (which is assumed to be zero since the object is at rest)
- ( a ) is the acceleration
- ( t ) is the time
Given that the object is at rest initially, ( v_i = 0 ).
Let's calculate the displacement along the x-axis (( \Delta x )):
[ \Delta x = x_B - x_A = 3 - 6 = -3 ]
Now, plug in the values into the kinematic equation:
[ -3 = 0 + \frac{1}{2} \left(\frac{4}{3}\right) t^2 ]
Solving for ( t ):
[ -3 = \frac{2}{3} t^2 ]
[ t^2 = \frac{-3 \times 3}{2} ]
[ t^2 = -\frac{9}{2} ]
Since time cannot be negative, it implies there's an issue with the given information or the problem setup. Typically, with a constant positive acceleration, the object would never reach point B as its position would continue to increase indefinitely. Therefore, the provided problem is not feasible in its current form.
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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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