# An object is at rest at #(1 ,8 ,4 )# and constantly accelerates at a rate of #5/4 m/s^2# as it moves to point B. If point B is at #(1 ,5 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

##### 1 Answer

#### Answer:

2.25 seconds

#### Explanation:

First thing is to determine the distance to be travelled. We can do this thanks to our old pal Mr. Pythagoras:

Now, we are given acceleration:

Integrate once, and we get v(t):

constant of integration c1 would represent initial velocity. We are told our mass it at rest at time t = 0, so c1 = 0.

Integrate a second time, and we get position x(t). (x as a function of t).

We will interpret c2 as the fraction of the distance s (that we calculated above) where the mass will start at. I.e, it's initial position at time t=0. It's at the start point at that time, so it has travelled zero percent of the distance (

But now we have everything we need. We know distance, so we can solve for time.

so, just a little algebra: