Suppose you drive down the road at a constant 420 kmh...

Suppose you drive down the road at a constant 42.0 km/h. Suddenly, you see a deer 16.0 m ahead of you. Your reaction time, before you hit the brakes, is 0.220 s. Then you decelerate at a constant 6.15 m/s? until you stop. (a) Do you hit the deer? If yes, at what speed do you hit the deer? If no, how far from the deer do you get to stop? (b) What is the fastest you can travel (in km/h) and not hit the deer? Answer both parts! All the questions

Transcript

00:01 In this video, i'm going to be looking at a problem in dealing with one -dimensional kinematics.

00:06 Okay, so what we have is we're driving on a horizontal road with some constant velocity.

00:12 Okay, so we're driving along.

00:17 Here's our car.

00:20 Okay, and we're moving with some v -sub -zero in the, i'll call this the positive x direction.

00:26 Right, then we notice a deer in the road.

00:30 There's this little deer head sorry, i can't draw okay, that deer is some distance d in front of us okay, so we notice the deer we take 0 .5 seconds to apply our brakes okay, that's our reaction time and then we decelerate with a constant acceleration a until we come to a stop and what we want to find is the distance between the deer and the car when we finally stop, and we want to find the maximum velocity, be sub -initial that we can be driving at and still not hit the deer.

01:10 Okay, so let's write to time some numbers first.

01:12 I have my initial velocity, and that equals 18 meters per second.

01:19 Okay, i have my distance between the car and the deer when the driver notices the deer, and that is 32 meters.

01:29 Okay, i have my reaction time, we already said delta t that equals 0 .5 seconds.

01:38 Okay and my head i have my deceleration or acceleration a that equals negative 10 meters per second.

01:48 So the first thing i want to find is, and i'll call this d1, is the distance that i continue traveling at my initial velocity of 18 meters per second before i put on the brakes.

02:00 Okay.

02:01 So that's going to be my reaction.

02:02 Time.

02:03 So that's just going to be my initial velocity times delta t.

02:08 Okay, 18 meters per second times a half a second gives me nine meters.

02:15 Okay, so that's how far i travel before i put on my brakes.

02:18 Then to find the distance i travel after applying the brakes, i'm going to use the equation v final squared equals v initial squared plus two times xxcule.

02:33 Acceleration times distance, okay, and i'll call this d2.

02:37 That's going to be our distance f that we take to come to a stop once we apply the brakes.

02:43 All right, i know my final velocity is going to be zero.

02:47 Okay.

02:49 So my distance d2 is going to equal my v initial squared divided by two times a.

03:01 Okay.

03:01 Note that when i bring this v initial squared over it becomes negative.

03:05 My acceleration is also negative, so those two cancel out.

03:09 We'll get a positive number for distance, and this gives me a distance of 16 .2 meters.

03:18 Okay, so the total distance, it takes me to come to a stop, and i'll call that d sub s...

Question

Please give Ace some feedback