Question

An object is at rest at `(2 ,9 ,5 )` and constantly accelerates at a rate of `1/5 m/s` as it moves to point B. If point B is at `(6 ,2 ,7 )`, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Answer 1

`t = 9.11` `"s"`

Explanation:

NOTE: I'll assume the given acceleration is `1/5` `"m/s"^2`, not `1/5` `"m/s"`.

We're asked to find the time `t` it takes an object to travel a certain distance with a given constant acceleration.

To do this, we can use the equation

`Deltax = v_(0x)t + 1/2a_xt^2`

where

• `Deltax` is the distance it travels, which can be found using the distance formula:

`Deltax = sqrt((6-2)^2 + (2-9)^2 + (7-5)^2) = 8.31` `"m"`

• `v_(0x)` is the initial velocity, which is `0` since it started from rest

• `t` is the time (we're trying to find this)

• `a_x` is the constant acceleration (given as `1/5` `"m/s"^2`)

Plugging in known values, we have

`8.31` `"m"` `=0t + 1/2(1/5color(white)(l)"m/s"^2)t^2`

`t = sqrt((8.31color(white)(l)"m")/(1/10color(white)(l)"m/s"^2)) = color(red)(ul(9.11color(white)(l)"s"`