00:02
So this question concerns two different kinds of motion that are happening at the same time.
00:08
We have one object, car a, which is undergoing constant acceleration motion, and another object, car b, which is undergoing constant velocity motion.
00:16
So we'll use the appropriate equations for each motion to determine how far each vehicle travels, and then we'll figure out the distance d between them by subtracting those distances.
00:28
And we're going to use the quantities as they came to us.
00:31
As long as we're careful about our units, we can use the quantities of 60 km per hour, 70 km per hour, etc., without having to do conversions, as long as our acceleration is given in those similar units as well.
00:48
So, let us do the constant acceleration motion of car a, and let us determine how long it takes for car a to stop.
00:58
We have this formula, that the final velocity of something that's moving with constant acceleration is equal to the initial velocity of the object, this is for car a, then, plus the acceleration times the time.
01:18
And so, we know that the time we're trying to find is for the car to come to a complete stop.
01:25
So the final velocity is going to be zero, and so the zero is going to equal the initial velocity of the car, plus the acceleration times the time.
01:37
So, if we bring the velocity over to the left -hand side, this gives us a negative va, is equal to a times t, and therefore, if you want to solve for the time, it's going to be a negative va, divided by the acceleration, is going to give us the time...