How does initial velocity affect a car's stopping distance?

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Homework Help Overview

The discussion revolves around the relationship between initial velocity and stopping distance for a car under constant braking force, specifically comparing a scenario where the car travels at 7 m/s versus 14 m/s.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of equations of motion to relate initial velocity, final velocity, acceleration, and distance. Questions arise regarding the correctness of the applied methods and the implications of changing initial velocity on stopping distance.

Discussion Status

Some participants have provided hints and guidance regarding relevant equations. There is an ongoing exploration of the implications of doubling the initial velocity on stopping distance, with some participants confirming the approach taken by others.

Contextual Notes

Participants are working under the assumption of a constant braking force and are discussing the implications of this assumption on the calculations and results.

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A car is traveling at 7 m/s when the wheels are locked up. The car slides 1.5 meters before coming to rest. If the car had been moving at 14 m/s, how far would the car slide, assuming the same breaking force is used?

Not sure where to go with this problem...
 
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Hint: Which of the equations of motion relates initial velocity, final velocity, acceleration, and distance moved?
 
I used the equation v^2=Vo^2+2(a)(S-So) and solved for acceleration, then plugged in new value for initial velocity and used the found acceleration. Is this correct?

accel. = -16.3m/s^2
distance traveled @ 14 m/s = 6.01 m
 
public_enemy720 said:
I used the equation v^2=Vo^2+2(a)(S-So) and solved for acceleration, then plugged in new value for initial velocity and used the found acceleration. Is this correct?

accel. = -16.3m/s^2
distance traveled @ 14 m/s = 6.01 m
Close enough, and that's exactly the correct approach. Since the velocity doubled, the stopping distance would be 2^2 = 4 times as great for the same acceleration.
 

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