00:01
All right, so the question gives us our car and a police car both traveling at 120 kilometers per hour and the police car is 25 meters in front of us.
00:08
So i'm going to convert that to meters per second, which is 33 .33 meters per second.
00:14
And let's write out what we have here.
00:17
So our initial exposition for us is zero meters.
00:23
Our initial velocity is 33 .33 meters per second.
00:30
And our acceleration right now, zero.
00:34
The police car, it's 25 meters, the same speed, and the acceleration is negative 5 .2 meters per second squared.
00:50
So we're going to use the equation.
00:53
Position is equal to your initial position, plus your initial velocity, plus one -half, your acceleration times your time squared.
01:04
So, for part a, it's asking the difference in position when t is equal to two seconds.
01:14
So plugging in our equation really quick for us, or for our car, we have our position is equal to zero plus 33 .33 times two plus zero because our acceleration is zero, so that part cancels out.
01:31
So our position is 66 .66 meters.
01:35
And for the police car, we have x is equal to 25 plus 33 .33 times 2 plus 1 half times negative 5 .2 times 2 to the power of 2, which gives the police car's position as 81 .26.
01:59
And the difference between that is 14 .6 meters.
02:06
For part a, after two seconds, that is their time.
02:10
For part b, let's first find the position of each car at t equals 2 .5 seconds.
02:18
So using the same formula as above for us, we get 0 plus 33 .33 times 2 .5 plus 0 .0.
02:32
So our position is 83 .325 meters.
02:43
For the police car, do the same thing.
03:02
So let me cut us out real quick...