00:01
All right, so let's say the position as a function of time of a particle is given by 13t squared minus 4 t cubed.
00:09
And so we want to find the position, velocity, and acceleration at five seconds.
00:15
So the position at five seconds is just going to be 13 times 25 minus 4 times 125.
00:24
So this would be negative 175, and i think it's in meters.
00:28
And then the velocity as a function of time, we can see is going to be 26t minus 12 t squared.
00:37
So the velocity at five seconds, 26 times 5 minus 12 times 25.
00:44
So this is negative 170 meters per second.
00:48
And then the, oops, excuse me, the acceleration as a function of time is going to be 26 minus 24t.
00:57
T, so the acceleration at five seconds is 26 minus 24 times 5, so negative 94 meters per second squared.
01:10
And then part d, we want to compute the maximum positive coordinate reached by the particle.
01:18
So this is where the velocity is zero.
01:21
And we can see the velocity is zero only at, so the velocity is zero at two different times.
01:27
Is at the origin.
01:30
So if we solve for this, what we'll have is 26 equals 12t.
01:36
So t is going to be 13 over 6 seconds.
01:41
And so x of 13 over 6, if we plug that in, 13 divided by 6, let's see, squared times 13 minus 4 times that cubed...