Question

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

Answer 1

`t = 6.51` `"s"`

Explanation:

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

To do this, we can use the equation

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

We know it starts from a state of rest, so the initial velocity `v_(0x)` is zero, so our equation now becomes

`Deltax = 1/2a_xt^2`

To find the displacement `Deltax`, we need to find the distance between the two coordinate points, which is done by the distance formula:

`Deltax = sqrt((1-4)^2 + (9-4)^2 + (1-5)^2) = color(red)(7.07` `color(red)("m"`

And our acceleration is given as `1/3` `"m/s"^2`

Plugging in known values and solving for `t`, we have

`t = sqrt((2Deltax)/(a_x)) = sqrt((2(color(red)(7.07)color(white)(l)color(red)("m")))/(1/3color(white)(l)"m/s"^2)) = color(blue)(6.51` `color(blue)("s"`