Solving for Car Speed and Stopping Time in a Braking Scenario

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SUMMARY

The discussion focuses on solving a physics problem involving a car's braking scenario, specifically calculating the initial speed and stopping time given a deceleration of 10 ft/s² and a stopping distance of 300 ft. The relevant equations used are the SUVAT formulas: v² - v₀² = 2as and v - v₀ = at. The solution confirms that the numerical answers derived from these equations are correct, emphasizing the appropriateness of using standard formulas over integration in this context.

PREREQUISITES
  • Understanding of kinematics, specifically SUVAT equations.
  • Familiarity with concepts of acceleration and deceleration.
  • Basic algebra skills for solving equations.
  • Knowledge of units of measurement, particularly feet and seconds.
NEXT STEPS
  • Review the derivation and application of SUVAT equations in various scenarios.
  • Explore real-world applications of kinematics in automotive safety and design.
  • Learn about the effects of different deceleration rates on stopping distances.
  • Investigate the role of friction in braking performance and stopping time.
USEFUL FOR

Students studying physics, automotive engineers, and anyone interested in understanding the dynamics of vehicle braking and stopping distances.

Alexanddros81
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Homework Statement


11.9 The brakes of a car are applied, causing it to slow down at a rate of ##10 ft/s^2##.
Knowing that the car stops in 300 ft, determine (a) how fast the car was traveling immediately
before the brakes were applied, (b) the time required for the car to stop

Homework Equations


Vector Mechanics Dynamics Beer P11_9.jpg


The Attempt at a Solution



Vector Mechanics Dynamics Beer P11_9 s.jpg

[/B]
Can you check my solution?
 

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Acceleration is constant, so your integration leads to the standard SUVAT formulas, that you may be expected to know:

##v^2 - v_0^2 = 2as##

##v - v_0 = at##

Not that integrating is wrong, but it's unusual to see it in these cases.

Your numerical answers look right.
 
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