An object is at rest at #(6 ,7 ,2 )# 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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Answer 1 · 2018-03-27T08:11:24

#t=3.24#

You can use the formula #s=ut+1/2(at^2)#
#u# is initial velocity
#s# is distance travelled
#t# is time
#a# is acceleration

Now, it starts from rest so initial velocity is 0

#s=1/2(at^2)#

To find s between #(6,7,2)# and #(3,1,4)#
We use distance formula
#s=sqrt((6-3)^2+(7-1)^2+(2-4)^2)#
#s=sqrt(9+36+4)#
#s=7#

Acceleration is #4/3# meters per second per second

#7=1/2((4/3)t^2)#
#14*(3/4)=t^2#
#t=sqrt(10.5)=3.24#