00:01
Indefinite and find the indefinite integral of the equation we're given so what we can do is d t is equal to the indefinite integral we're trying to find that t minus two so that'd be our question and now we just got to take the anti -derivative so this would equal this would equal t minus one over minus one minus t equals one over minus one of t minus t plus c because it is an indefin integral although we won't have to worry about the c later on because we just we we don't need to use it now if we're trying to find the displacement okay if we're trying to find the displacement all we got to do is find a displacement so to do that we got to find the integral over the interval of 0 .5 to 2 so we can just go 0 .5 to 2 vt d t is equal to we can skip a few steps here because we already know what the anti -derivative of this is so we can just write this as minus 1 over t minus t from 0 .5 to 2 and if i bring this up here we can just solve this right side out and we would get we would get um minus 1 over 2 minus 2 minus 2 minus 1 over 0 .5 minus 0 .5, and this equals minus 2 .5 minus 2 .5, which equals 0.
01:41
So that would mean our displacement over the interval from 0 .5 to 2 is just 0 meters.
01:50
Okay, so we did the first half of that question.
01:53
Now to do the second half, which would be finding the distance, we first need to figure out when it is that t, when the equation via t, switches signs.
02:06
So what do i mean by this? well, how do we, importantly, how do we solve for this? because we want to know when the distance is negative and when the distance is positive, so when it's going backwards and forwards.
02:20
So do that, we can just first find out when t equals zero.
02:25
So that would be t minus 2 minus 1 equals 0.
02:29
So first we let's solve for t.
02:31
So, t, so this would be 1 over t squared equals 1, 1 equals t squared.
02:40
So that would mean plus or minus 1 is equal to t because we just score every both sides...