00:01
There are two cars on a highway, both traveling at the same velocity, but then car b, which is 50 meters behind car a, decides to accelerate for seven seconds.
00:11
We would like to find the final velocity, the acceleration of, and the displacement of the passing car.
00:18
So to start it out, we can first visualize the problem by looking at a graph of distance versus time.
00:25
And for car a, we can see that it started 50 meters ahead of car b, and it's starting 50 meters ahead of car b, line is linear because it's traveling at a constant velocity.
00:34
And then for carb starts at zero, and it is a parabola because it's accelerating until the seven second mark, and then it becomes linear again.
00:44
But, you know, it is traveling faster than cara because of the acceleration.
00:49
So next to find the acceleration of carb, we need our kinematic equations, such as the final distance, xf, is equal to the initial distance.
01:00
Oh, not multiple.
01:02
But equal to the initial distance plus the initial velocity times the time plus one half the acceleration times the time squared.
01:18
So as you can see we are just missing a, so we can go ahead and solve for that minus x not minus v not t and then xf minus x not t and then xf minus x not minus v not t and then xf minus v not t is equal to one half a t squared, and then solving for a, we get 2 over t squared times the quantity xf minus x -0, minus v -t.
01:54
And then before we plug in any of our numbers, we should go ahead and check our units.
01:58
1 over 2nd squared, meters minus meters minus miles, and hour.
02:06
Times second.
02:09
And so we want this to be meters a second so we can get the appropriate units of meters a second squared for our acceleration...