An object is at rest at #(1 ,5 ,1 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(9 ,4 ,8 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Question

1240 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-16T22:01:56

#t~=4" s"#

#A=(1,5,1)" the point of A"#

#B=(9,4,8)" the point of B"#

#A_x=1" "A_y=5" "A_z=1#

#B_x=9" "B_y=4" "B_z=8#

#"let's calculate distance between the points A and B"#

#Delta s=sqrt((B_x-A_x)^2+(B_y-A_y)^2+(B_z-A_z)^2)#

#Delta s=sqrt((9-1)^2+(4-5)^2+(8-1)^2)#

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

#Delta s=sqrt(64+1+49)#

#Delta s=10,68" m"#

#a=4/3 m/s^2 "acceleration of object"#

#t="elapsed time from the point of A to the point of B"#

#Delta s=1/2 *a*t^2#
#"distance equation for an object moving from rest"#

#10,68=1/2*4/3*t^2#

#t^2=(3*10,68)/2#

#t^2=16,02#

#t~=4" s"#