Car's Total Acceleration on Curved Road: Calculate Magnitude

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Discussion Overview

The discussion revolves around calculating the total acceleration of a car traveling along a curved road, with a focus on understanding the components of acceleration due to both tangential and radial factors. Participants explore the application of kinematic equations and vector addition in the context of this problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem and seeks hints rather than direct answers.
  • Another participant suggests defining the distance along the road as 's' and notes the constant tangential deceleration of -0.6 m/s².
  • Discussion includes the use of kinematic formulas relating final velocity, initial velocity, constant acceleration, and distance traveled.
  • Participants discuss the relationship between normal acceleration, velocity, and radius of curvature.
  • One participant calculates the final velocity at point B to be 10.58 m/s and proposes an acceleration value of 1.87 m/s² based on this velocity.
  • There is a correction regarding the need to find the total (resultant) acceleration rather than just the radial component.
  • Another participant incorrectly combines the tangential and radial accelerations as scalars, leading to confusion about vector addition.
  • A later reply suggests a resultant acceleration value of 1.96 m/s², which is affirmed by another participant.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct method for calculating total acceleration, particularly regarding vector addition versus scalar addition. There are competing views on the final values for acceleration, indicating unresolved disagreements.

Contextual Notes

Participants reference various kinematic equations and concepts, but there are limitations in the discussion regarding the application of vector addition and the assumptions made about the components of acceleration.

jaymar023
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A car travels along a level curved road with a speed which is decreasing at a constant rate of 0.6 m/s. The speed of the car as it passes point A is 16 m/s. Calculate the magnitude of the total acceleration of the car as it passes point B which is 120 m along the road from A. The radius of curvature of the road at B is 60 m.

I am clueless about how to solve this question so if anybody can give me any hints or tips (not the answer) it would be much appreciated.
 
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jaymar023 said:
A car travels along a level curved road with a speed which is decreasing at a constant rate of 0.6 m/s. The speed of the car as it passes point A is 16 m/s. Calculate the magnitude of the total acceleration of the car as it passes point B which is 120 m along the road from A. The radius of curvature of the road at B is 60 m.

Hi jaymar023! :smile:

(you mean 0.6m/s2)

Hint: call the distance along the road s.

Then you know s'' = -0.6.

And s = rθ. So θ'' = … ?

Now what are the tangential and radial accelerations in terms of r and θ? :smile:
 
jaymar023: The problem statement gives you a constant tangential deceleration, -0.6 m/s^2 (assuming that's what you meant to type). Do you know of a kinematics formula that relates final velocity, initial velocity, constant acceleration, and distance traveled? Also, look for a second formula that relates normal acceleration, velocity, and radius of curvature.
 
acceleration = change in velocity / time and acceleration = velocity2/ radius ?
 
actually v2= u2 + 2as ?
 
So the final velocity is 10.58 m/s and the acceleration at point B = 1.87 m/s2 ?
 
jaymar023 wrote,[/color] "v^2 = u^2 + 2*a*s, and acceleration = (velocity^2)/radius? ... So the final velocity is 10.58 m/s?"[/color]

That's correct. Normal acceleration = (velocity^2)/(radius of curvature).

jaymar023 wrote,[/color] "And the acceleration at point B = 1.87 m/s^2?"[/color]

Not quite. The question is asking for total (resultant) acceleration.
 
So the resultant acceleration is -0.6 m/s2 + 1.87 m/s2 = 1.27m/s2?
 
That's incorrect. Study "vector addition" in your textbook, and how to compute the magnitude (length) of the resulting vector when you add two vectors together. Vector addition is not the same as scalar addition.
 
  • #10
Answer is 1.96m/s^2?
 
  • #11
That's correct.
 

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