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
ali ergin
Mar 20, 2016

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"

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