An object is at rest at #(8 ,7 ,3 )# and constantly accelerates at a rate of #1/4 m/s^2# as it moves to point B. If point B is at #(1 ,3 ,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 · 2016-03-29T18:26:37

#t=8,06 " s"#

#"Point A=(8,7,3) Point B=(1,3,4")#
#"distance between the Point A and B :"#

#s=sqrt((1-8)^2+(3-7)^2+(4-3)^2)#

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

#s=sqrt(49+16+1)" "s=sqrt66#

#s=8,12 " m"#

#"equation for an object constantly accelerating from rest"#

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

#t^2=(2s)/a#

#a=1/4 " "m/s^2#

#t^2=(2*8,12)/(1/4)#

#t^2=2*8,12*4=64,96#

#t=8,06 " s"#