# An object is at rest at #(2 ,8 ,6 )# and constantly accelerates at a rate of #5/3 m/s^2# as it moves to point B. If point B is at #(7 ,5 ,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.

so,

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To find the time it takes for the object to reach point B, use the kinematic equation: ( \Delta d = v_i t + \frac{1}{2} a t^2 ). The initial velocity ((v_i)) is zero since the object is at rest. Rearrange the equation to solve for time ((t)): (t = \sqrt{\frac{2 \Delta d}{a}}). Substitute the coordinates and acceleration values to calculate the time. The result is approximately 5.77 seconds.

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