Question

An object is at rest at `(8 ,3 ,6 )` and constantly accelerates at a rate of `1/4 m/s^2` as it moves to point B. If point B is at `(6 ,8 ,2 )`, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Answer 1

It will take `4.23` seconds.

Explanation:

The distance between two points `(x_1,y_1,z_1)` and `(x_2,y_2,z_2)` is given by

`sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`

Hence distance between `(8,3,6)` and `(6,8,2)` is

`sqrt((8-6)^2+(3-8)^2+(6-2)^2)`

= `sqrt(2^2+5^2+4^2)=sqrt(4+25+16)=sqrt45=3sqrt5`

(As distance covered is given by `S=ut+1/2at^2`, where `u` is initial velocity, `a` is accelaration and `t` is time taken. If body is at rest `S=1/2at^2` and hence `t=sqrt((2S)/a)`

As the coordinates are in meters, the time taken at an acceleration of `1/4` `m/sec^2` will be given by

`t=sqrt((2xx3sqrt5)/(1/4))=sqrt(4xx2xx2.236)=sqrt(17.888)=4.23`