Question

An object is at rest at `(7 ,9 ,4 )` and constantly accelerates at a rate of `7/4 m/s^2` as it moves to point B. If point B is at `(5 ,1 ,8 )`, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Answer 1

`t = 3.24` `"s"`

Explanation:

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

We can use the equation

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

where

• `Deltax` is the change in position of the object, which is simply the distance between the two coordinate points:

`Deltax = sqrt((5"m" - 7"m")^2 + (1"m" - 9"m")^2 + (8"m" - 4"m")^2)`

`= 9.17` `"m"`

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

• `t` is the time, which is what we're trying to find, and

• `a_x` is the acceleration, which is `7/4` `"m/s"^2`.

Plugging in known variables we have

`9.17"m" = (0)t + 1/2(7/4"m/s"^2)t^2`

`9.17"m" = (7/8"m/s"^2)t^2`

`t^2 = (9.16"m")/(7/8"m/s"^2)`

`t = sqrt((9.16"m")/(7/8"m/s"^2)) = color(red)(3.24` `color(red)("s"`

The object will travel the distance in `color(red)(3.24` seconds