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.

Question

1206 views around the world

You can reuse this answer
Creative Commons License

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"#