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.

1 Answer
Nathan L.
Jul 2, 2017

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"

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