You're driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10 m/s². a. How much distance is between you and the deer when you come to a stop?

Video transcript

Hey, everyone in this problem, a race pilot driving at a speed of 35 m/s, notice the presence of a competitors car crashing 100 m in front of him. The pilot applies a negative acceleration of 9m/s squared. When the race car is totally at rest, were asked to determine the distance separating it from the crash, were told to suppose that a race pilots typical reaction time is 0. seconds. The answer choices were given our A seven m B 25 m C 68 m D 75 m. Now this is a motion problem. We're given information about um some acceleration, some speed, some distances and sometimes we have a uniform acceleration. And so what we expect to do is to use our Kinnah Matic or U A M equations. Now, in order to do that, we need to consider our five variables. So let's write out the information that we know and see what we have. We have an initial speed of our race car of m per second. So V nought is 35 m per second. The final speed of the car is going to be 0m per second because we want it to come to a stop. Okay. It sees that crash, we wanted to come to a stop before hitting that crash. The acceleration we're given is nine m per second squared. We're told that it's a negative acceleration. And so we have negative nine m per second squared. And that makes sense in order to stop, we would need to apply a negative acceleration. And what we want to find is we want to find the distance separating the car from the crash. So we know the total distance to the crash. So let's find the distance it takes to stop and then we can calculate that difference. And so the distance here is what we're looking for. We aren't given information about the time T and that's not really what we're looking for. So what were we want to do? We have three known values and one unknown that we're trying to find begin, go ahead and choose our um equation that doesn't include the time T plug in our values and solve for that distance. And that equation is going to be the following V L squared is equal to B not squared Plus two multiplied by the acceleration multiplied by the distance D the final speed is zero. So on the left hand side, we have zero right hand side, we have 35 m per second squared plus two multiplied by negative nine m per second squared times the distance D we're looking for, we can move this two multiplied by negative eight m per second squared D term to the left hand side. In order to try to isolate D it's going to give us m per second squared, multiplied by D on the left hand side and 1225 m squared per second squared. On the right hand side, we divide by 18 m per second squared and we get a distance d of 68. repeated meters. So this is the distance we found and we have to be careful. This is not the answer. Okay. It can be really easy to say. I found a distance. The questions asking for a difference. Here's the answer. Remember the question asking us to find the distance separating the car from the crash, not the distance that the car traveled. The other thing we have to note is that the race pilot has a reaction time. So the total time or the total distance the car travels before it stops is going to be this distance we've calculated. Well, it's decelerating but also the distance it traveled during its reaction time. Okay. So let's get into the distance the car travels during this race pilots reaction time. Now, during that reaction time, we are going to be traveling at a constant speed. And so we only have three variables to consider. We have the speed V, Which we know is 35 m/s. We have the distance D, which is what we're looking for. And let's call this D R the distance during the reaction time. And we have the time T and we're going to call this tr the response time. And we're told that the response time for a race pilot is 0.2 seconds. Now because we have constant speed. The equation governing this motion is going to be, the speed is equal to the distance. In this case, D R over the time tr Our speed is 35 m/s. That's equal to the distance divided by the time, 0.2 seconds. This tells us that our distance during the response time is going to be 35 m per second times 0. seconds for a distance D R of seven m. Alright. So we found two distances, we found the distance that the car traveled while the pilot is responding. The race pilot is responding. We found the distance that the car travels while they're decelerating. What's that total distance of car traveled? The total distance the car travel is gonna be equal to the sum of the two D plus D R which is equal to 68. m plus seven m, giving ourselves some more space to work. This is equal to 75.055 repeated m. Now we have to be careful once more. This isn't our final answer. The final answer asked how far we were from the crash. So this is how far we traveled. The crash was initially 100 m in front of us. And so the distance between the car And the crash is gonna be that initial 100 m, we were away minus the 75.55 repeated meters we traveled trying to stop, Okay. And this is gonna give us a distance of approximately m. Alright. So now we have the correct distance we were looking for if we go back up to our answer choices, Okay. We found that the distance separating the car from the crash once it was at rest was 25 m which corresponds with answer choice. B thanks everyone for watching. I hope this video helped see you in the next one.