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.

Answer 1

#~~3.25s#

Here displacement = linear distance between the given points so displacement #s=sqrt((6-3)^2+(5-1)^2+(9-4)^2)=sqrt50m=5sqrt2m# Initial velocity #u=0# Acceleration #a=4/3ms^-2# time taken t=?
So #s=ut+1/2at^2# #5sqrt2=0*t+1/2*4/3t^2# #t^2=3/2*5sqrt2~~10.6# #t ~~sqrt10.6~~3.25s#
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Answer 2

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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Answer from HIX Tutor

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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