An object is at rest at #(4 ,1 ,6 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(3 ,5 ,7 )#, 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 · 2016-04-08T17:06:29

#t=2,52 " s"#

#"the point of A:(4,1,6)"#
#"the point of B:(3,5,7)"#

#"distance between the point A and B :"#
# s=sqrt((A_x-B_x)^2+(A_y-B_y)^2+(A_z-B_z)^2) #

#s=sqrt((4-3)^2+(1-5)^2+(6-7)^2)#

#s=sqrt(1^2+(-4)^2+(-1)^2)#

#s=sqrt(1+16+1)=sqrt18#

#s=4,24" m"#

#"distance equation for an object starting from rest:"#

#s=1/2*a *t^2#

#"a:acceleration of object"#

#"t:elapsed time"#
#"given "a=4/3 m/s^2#

#4,24=1/2*4/3*t^2#

#t^2=(6*4,24)/4#

#t^2=6,36#

#t=2,52 " s"#