Find deceleration, given initial velocity and final distance

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SUMMARY

The discussion centers on calculating the deceleration of a car that skids to a stop from an initial velocity of 88 ft/s over a distance of 176 ft. The initial attempt incorrectly assumed constant velocity, leading to a calculated deceleration of -44 ft/s². The correct approach involves using kinematic equations for constant acceleration, which yield a deceleration of -22 ft/s² as confirmed by the textbook answer. This highlights the importance of applying the right kinematic principles in physics problems.

PREREQUISITES
  • Understanding of kinematic equations for constant acceleration
  • Basic calculus for integration and differentiation
  • Familiarity with initial and final velocity concepts
  • Knowledge of units of measurement in physics (e.g., feet per second)
NEXT STEPS
  • Study kinematic equations, specifically those relating to constant acceleration
  • Learn how to derive motion equations from basic principles of physics
  • Explore the concept of integration in the context of motion
  • Review examples of real-world applications of deceleration calculations
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in automotive engineering or safety analysis, particularly those focusing on motion dynamics and deceleration calculations.

EricPowell
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Homework Statement


A car traveling at 88ft/s skids 176ft after its brakes are applied. The deceleration provided by the braking system is constant. What is its value?

The Attempt at a Solution


$$
v_0=88 \\
v_f=0 \\
d_0=0 \\
d_f=176
$$
$$
d(t)=\int88\,dt \\
d(t)=88t+c \\
0=88(0)+C \\
C=0 \\
176=88t \\
t=2s
$$
$$
a=\frac{Δv}{Δt} \\
=\frac{-88}{2} \\
=-44ft/s
$$
The answer key of the textbook says that the deceleration is -22ft/s2. :(
 
Physics news on Phys.org
You have assumed motion with constant velocity in finding d(t). You need to use the kinematic relationships that deal with motion with constant acceleration:
http://hyperphysics.phy-astr.gsu.edu/hbase/acons.html

Those should give you 2 equations in 2 unknowns.
 

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