I think I solved this whole thing but it seems a bit too simple. I think I might've missed a detail somewhere. This is the problem, followed by my steps:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Two cars are about hit each other (face to face). The first car is doing 20m/s and decelerating at a rate of 5m/s^2 while the second car is doing 15m/s decelerating at a rate of 7.5m/s^2. When the drivers realize their situation the cars are 25 meters apart.

1. Find the moment (after how many second) will the crash happen.

2. What distance did the first car do before hitting the second car?

3. What is the speed of both cars as they hit each other?

3. The attempt at a solution

1. Find the moment (after how many second) will the crash happen.

Car A

Info: 20m/s, deceleration 5m/s^2 (a=-5m/s^2)

Function: x=xi+(vi*t)+0.5(at^2)

xi = 0, vi = 20m/s, t is time, a is -5m/s^2 so I simplified it to:

x = 20t - 2.5t^2

Car B

Info: 15m/s, deceleration 7.5m/s^2 (a=-7.5m/s^2)

Function: x=xi+(vi*t)+0.5(at^2)

xi = 0, vi = 15m/s, t is time, a is -7.5m/s^2 so I simplified it to:

x = 15t - 3.75t^2

What I did after is simply plug in 't' (0, 1, 2...) into each function until their sum was greater than 25m (the distance that initially separated both vehicles). I found that after 1 second:

xa(1) = 20(1) - 2.5(1^2) = 17.5 meters

xb(1) = 15(1) - 3.75(1^2) = 11.25 meters

Total: 28.75 meters, which is greater than 25, the cars hit each other a bit before 1 second.

This seem a bit too easy... but I kept going anyways.

2. What distance did the first car do before hitting the second car?

I got this from the first question. 17.5 meters. This is where I started realizing my first part might've been wrong. I was expecting the problem to be a bit more precise. Yes, if the car drives for 17.5 meters it will hit the second car, but it actually hits it BEFORE that so 17.5 meters isn't a precise answer here.

3. What is the speed of both cars as they hit each other?

I found dx/dt of my first functions:

va(t) = 20 - 5t

vb(t) = 15 - 7.5t

Now that makes sense. The initial speed of each car, minus the deceleration rate * the amount of second they slowed down for.

speed of A: 15 m/s

speed of B: 7.5 m/s

Anyone notices if I did something wrong? I'm thinking maybe the functions I used may not be exactly what I think they are, but going through my notes I can't find anything more appropriate for the problem!

Thanks a lot!

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# Homework Help: Car collision with constant deceleration

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