A truck passes point a on a straight level road with a...

A truck passes point A on a straight level road with a constant velocity of 12 m/s. At the same instant, an automobile starts from rest at point A and travels in the same direction as the truck with a constant acceleration of 1.8 m/s2. How far beyond point A will the automobile overtake the truck? (AF: Round off to the nearest unit, no decimals) A truck passes point A on a straight level road with a constant velocity of 12 m/s. At the same instant, an automobile starts from rest at point A and travels in the same direction as the truck with a constant acceleration of 1.8 m/s2. If the speed limit on this road is 55 km/hr., is the automobile within the speed limit as it passes the truck? (AF: YES or NO)

Transcript

0:00 All right, hello.

00:01 In this question, we're given this setup where we have two vehicles, one and two.

00:05 And vehicle one has a constant speed of 12 meters per second when it passes point a.

00:11 And then at point a, we have vehicle two, which has a constant acceleration of 1 .8 meters per second, but initially starts at rest.

00:18 And we're going to find out how far beyond point a will the automobile or vehicle one overtake the truck.

00:24 So they're going to travel some distance, d.

00:28 And we want to figure out what this d is, such that it will be the same.

00:32 We know that they're going to get here at the same time as well.

00:36 So their delta t for this, delta t for one is going to equal delta t for two, because they're going to get there at the same time since they're covering the same distance.

00:46 And that's where they're going to meet.

00:47 So how are we going to find this here? well, we can use for vehicle one, we can use the idea that since there's a constant velocity, we know that the velocity is a change in distance over a change in time, which in this case is going to be distance over delta t.

01:03 And that will be for one, which will be the same for both.

01:05 So we have one equation with two unknowns.

01:08 And then we can also use an equation for, write an equation for vehicle two.

01:12 And so we can use the equation that the distance that that car traveled is going to be where it started, plus its initial speed times its time, plus 1 half times its acceleration times its time, or change in time squared.

01:25 We're going to say it starts at d equals zero.

01:27 And we're going to say it's not moving to start, because it isn't, it's just accelerating.

01:32 And so now we have d equals 1 half a delta t squared.

01:36 And this now has delta t and d are two unknowns.

01:41 And so we have two equations, two unknowns, and we can go ahead and solve this...

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