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

1 Answer
Mar 20, 2016

Answer:

#t=3,17 " s"#

Explanation:

#P_A=(color(red)(1),color(green)(3),color(blue)(5))" the point of A"#
#P_B=(color(red)(1),color(green)(9),color(blue)(8))" the point of B"#
#Delta x=color(red)(1-1=0)#
#Delta y=color(green)(9-3=6)#
#Delta z=color(blue)(8-5=3)#
#Delta s:"distance between the " P_A" and "P_B#

#Delta s=sqrt(Delta x^2+Delta y^2 +Delta z^2)#
#Delta s=sqrt(color(red)(0^2)+color(green)(6^2)+color(blue)(3^2))#
#Delta s=sqrt(color(green)(36)+color(blue)(9))#
#Delta s=sqrt 45" "Delta s=6,71" m"#
#"use the equation below:"#
#Delta s=1/2*a* t^2" a="4/3 m/s^2#
#6,71=1/2* 4/3*t^2#

#t^2=(6*6,71)/4#
#t^2=10,07#

#t=3,17 " s"#