An object is at rest at #(1 ,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 ,5 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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An object is at rest at #(1 ,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 ,5 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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Answer 1 · 2017-09-29T18:40:06

5.08 seconds

Explanation:

#A(1,2,1)# and #B(4,9,5)#
Displacement #AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#
#AB=sqrt((4-1)^2+(9-2)^2+(5-1)^2)=sqrt(3^2+7^2+4^2)#
#AB=sqrt(9+49+16)=sqrt74 m#

Acceleration #a=2/3 m/s^2#
Initial Velocity #u=0#

Using Newton's Second Equation
#S=ut+1/2at^2#
S is displacement
#sqrt74=0+1/2(2/3)t^2#
#2/3t^2=2sqrt74#
#t^2=3sqrt74#
#t=sqrt(3sqrt74)#
#t=5.08 "seconds"#

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An object is at rest at #(1 ,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 ,5 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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Explanation:

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