Question

An object is at rest at `(4 ,5 ,1 )` and constantly accelerates at a rate of `4/3 m/s^2` as it moves to point B. If point B is at `(7 ,9 ,2 )`, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Answer 1

2.77s

Explanation:

The coordinate of initial position of the object is`(x_1=4,y_1=5,z_1=1)`

The coordinate of final position of the object is`(x_2=7,y_2=9,z_2=2)`

Initial velocity of the object`u=0`
Acceleration `a=4/3m/s^2`

Distance traversed `s= sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`
`=sqrt((7-4)^2+(9-5)^2+(2-1)^2))`
`=sqrt(9+16+1)=sqrt26=5.1m`
If the time required be t sec then
`s=ut+1/2*a*t^2=0*t+1/2*4/3*t^2` `=>5.1=2/3*t^2`
`t=sqrt(15.3/2)=2.77s`