Question

An object is at rest at `(2 ,1 ,5 )` and constantly accelerates at a rate of `7/6 m/s` as it moves to point B. If point B is at `(6 ,3 ,7 )`, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Answer 1

`t = 2.90` `"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((2-6)^2 + (1-3)^2 + (5-7)^2) = 4.90` `"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 `7/6` `"m/s"^2`)

Plugging in known values, we have

`4.90` `"m"` `=0t + 1/2(7/6color(white)(l)"m/s"^2)t^2`

`t = sqrt((4.90color(white)(l)"m")/(7/12color(white)(l)"m/s"^2)) = color(red)(ul(2.90color(white)(l)"s"`