Question

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

Answer 1

5.08 seconds

Explanation:

`A(1,2,1)` and `B(4,9,5)`
Displacement `AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`
`AB=sqrt((4-1)^2+(9-2)^2+(5-1)^2)=sqrt(3^2+7^2+4^2)`
`AB=sqrt(9+49+16)=sqrt74 m`

Acceleration `a=2/3 m/s^2`
Initial Velocity `u=0`

Using Newton's Second Equation
`S=ut+1/2at^2`
S is displacement
`sqrt74=0+1/2(2/3)t^2`
`2/3t^2=2sqrt74`
`t^2=3sqrt74`
`t=sqrt(3sqrt74)`
`t=5.08 "seconds"`