An object is at rest at #(2 ,1 ,5 )# and constantly accelerates at a rate of #2 m/s# as it moves to point B. If point B is at #(6 ,3 ,7 )#, 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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Using the kinematic equation ( d = ut + \frac{1}{2}at^2 ), where ( d ) is the displacement, ( u ) is the initial velocity, ( a ) is the acceleration, and ( t ) is the time, we can solve for ( t ). Since the object is at rest initially, ( u = 0 ).
Substituting the given values:
( 4 = 0 + \frac{1}{2} \cdot 2 \cdot t^2 )
Solving for ( t ):
( t^2 = \frac{4}{2} )
( t^2 = 2 )
( t = \sqrt{2} ) seconds
So, it will take approximately ( \sqrt{2} ) seconds for the object to reach point B.
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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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