How Do You Calculate the Moment When Speed Changes in a Decelerating Car?

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SUMMARY

The discussion focuses on calculating the moment when a decelerating car's speed changes from 100 km/h to 10 km/h using the formula L(t) = At - Bt², where B is defined as 90 km/h². Participants emphasize the importance of understanding derivatives to find the time at which the speed changes and the car's acceleration at that moment. The conversation suggests using introductory physics textbooks, such as Halliday, Resnick, and Walker, for foundational knowledge and problem-solving techniques related to motion and acceleration.

PREREQUISITES
  • Understanding of calculus, particularly derivatives
  • Familiarity with kinematic equations of motion
  • Basic knowledge of velocity and acceleration definitions
  • Access to introductory physics textbooks, such as Halliday, Resnick, Walker
NEXT STEPS
  • Learn how to apply derivatives in kinematic equations
  • Study the relationship between distance, velocity, and acceleration
  • Explore the concept of constant acceleration in physics
  • Review sections on acceleration from reputable physics resources, such as Wikipedia
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This discussion is beneficial for physics students, automotive engineers, and anyone interested in understanding the principles of motion and acceleration in decelerating vehicles.

Danatron
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A Car, initially traveling at the speed 100 km/h, slows down according to the formula. L(t)= At - Bt^2
Where L is the traveled distance, t is the time & B= 90 km/h^2. Using derivative, find the time moment when the car speed becomes 10 km/h. Find the acceleration of the car at this moment.

i think this is a function (my interpretation below)

50(t)= 100t - 90t^2

would i just have to graph the function?

any guidance appreciated
 
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That formula for L(t) is reminiscent of a constant acceleration motion. So you can find the negative acceleration of the car by inspection (since you know B).

Why is there a 50t on the LHS of your equation?

What definitions of velocity and acceleration do you have? In particular, ones relating to position?
 
The car has a velocity of 100km/h and slows down to 10km/h?

The 50 was just a random distance number. Disregard it.
 
Danatron said:
The car has a velocity of 100km/h and slows down to 10km/h?
Yes. You can think of the situation as the car applying brakes and decelerating at a constant rate.
 
Do you know where i could do some reading to find out where to begin with this problem?
 
Do you have an introductory physics textbook? E.g see the first few chapters of Halliday, Resnick, Walker.

Related links:
Section 1 and 3.1 of http://en.wikipedia.org/wiki/Acceleration

If you want to understand things well though, nothing beats a good textbook and the accompanying problems.
 
If you know calculus, then the first derivative of distance is velocity, and the second derivative is acceleration.
 

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