Am I setting up this kinematic equation properly?

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Homework Help Overview

The discussion revolves around a kinematic problem involving a race car that accelerates from rest over a quarter mile and then comes to a stop after applying brakes. The participants are examining the setup of the kinematic equations and the implications of the values used in the calculations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the acceleration and final speed of the car, while expressing uncertainty about the stopping distance. Some participants question the relevance of the initial distance traveled when calculating the stopping distance after braking.

Discussion Status

Participants are actively discussing the implications of the braking acceleration and its practicality. There is a recognition that the values used may lead to unexpectedly large stopping distances, prompting further exploration of the braking acceleration's magnitude.

Contextual Notes

There is a focus on the assumptions made regarding the initial conditions and the braking scenario, particularly the interpretation of the initial position in the context of the stopping distance calculation.

TaylorHoward21
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A race car starts from rest and goes a quarter mile (1/4 mi) in 12.1 seconds. Assume the acceleration of the car is constant. (a.) What is the acceleration of the car? (b.) What is the final speed of the car? (c.) If you hit the brakes, how far would it take to stop the car if the breaks cause an acceleration of -2.00 m/s2?

I believe I have parts a and b right, however I am not confident with my process of solving part C.

1/4 mi ≈ 402.3 m

a.) acceleration = 5.5m/s^2
b.) Final speed (at 12.1 seconds) = 66.5 m/s

c.) For part C, I reset the known values to:
a = -2.00m/s2
V0 = 66.5m/s
V = 0 (because solving for car stop which is zero velocity)
X0 = 402.3m

The equation I used: v2 - V20 = 2a(x - x0)
The answer I got was 1507.8m = x
For a car going 66.5m/s that is slowing down at -2.00 m/s2 does this answer seem practical? I am struggling to check my work here.

Many thanks.
 
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TaylorHoward21 said:
X0 = 402.3m
It asks how far the car goes after hitting the brakes. The distance already traveled is not relevant.
 
haruspex said:
It asks how far the car goes after hitting the brakes. The distance already traveled is not relevant.
So if I change X0 to be = 0 the new answer I get is 1105.5m. This still seems rather far for a car to stop from 66.5m/s to 0m/s. Is -2.00m/s^2 simply just a very slow breaking acceleration?
 
TaylorHoward21 said:
Is -2.00m/s^2 simply just a very slow breaking acceleration?
It is rather modest. Safe but serious braking is about 0.5g on a dry road. Emergency braking could go as high as 0.7-1g, depending on the vehicle.

And it is "braking", using "brakes", not "breaking".
 
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