Question

An object is at rest at `(4 ,8 ,3 )` and constantly accelerates at a rate of `4/3 m/s^2` as it moves to point B. If point B is at `(3 ,1 ,7 )`, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Answer 1

`t=3,49 " s"`

Explanation:

`"The Point of A="(4,8,3)`
`"The Point of B="(3,1,7)`
`"distance between two point:"`
`s=sqrt((B_x-A_x)^2+(B_y-A_y)^2+(B_z-A_z)^2)`

`s=sqrt((3-4)^2+(1-8)^2+(7-3)^2)`

`s=sqrt((-1)^2+(-7)^2+4^2)`

`s=sqrt(1+49+16)" "s=sqrt66`

`s=1/2*a *t^2`
`"equation for object moving at constant acceleration from rest"`
`sqrt 66=1/2*4/3*t^2`
`6*sqrt66=4*t^2`
`6*8,12=4*t^2`
`48,72=4*t^2`
`t²=(48,72)/4`
`t^2=12,18`

`t=3,49 " s"`