Question

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.

Answer 1

`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"`