Using free fall acceleration to find another acceleration

In summary, the problem involves finding the acceleration of a new automobile in terms of g, given that it stops from a speed of 100 km/h in 41 m. Using the kinematics equation, the acceleration is calculated to be -9.4098 m/s^2 or -0.9602 g, indicating that the acceleration is slightly less than the free-fall acceleration of 9.81 m/s^2. However, the final answer should be rounded to the appropriate number of significant figures.
  • #1
garcia1
27
0

Homework Statement



A test of the prototype of a new automobile
shows that the minimum distance for a con-
trolled stop from 100 km/h to zero is 41 m.
Find the acceleration, assuming it to be
constant as a fraction of the free-fall accel-
eration. The acceleration due to gravity is
9.81 m/s2.
Answer in units of g.


Homework Equations



Kinematics equations


The Attempt at a Solution



I'm actually unsure how to even begin this problem. The statement has me confused, such as what they mean by "a fraction of the free-fall acceleration."
 
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  • #2
It means 9.8 m/s^2 would be 1g, 19.6 m/s^2 would be 2g, etc.

Do you know any kinematic equation that relates final speed, initial speed, acceleration, and distance?
 
  • #3
What I used with your advice was this equation:

v^2 = Vo^2 + 2ax -> a = v^2 - vo^2 / 2x -> 0 - (27.778 m/s^2) / 2(41m) = -9.4098

From here I did this equation as a fraction of the free fall acceleration:

-9.4098 m/s^2 / -9.80m/s^2 -> A = .9602g.

Whatever I might have done, I got the question wrong. Can you maybe help me elaborate on my errors?
 
  • #4
Your methodology is okay. The resulting acceleration value, whether or not in units of g, should still be negative. You might also want to pay attention to the number of significant figures that are warranted.
 
  • #5
Free fall acceleration, or the acceleration due to gravity, is a constant value of 9.81 m/s2. It is not clear what other acceleration they are referring to. Additionally, the given information about the prototype of a new automobile does not seem relevant to finding another acceleration. Can you please provide more context or clarify the problem?
 

1. What is free fall acceleration?

Free fall acceleration is the acceleration experienced by an object when it falls freely under the influence of gravity, without any other forces acting on it. It is constant on Earth and has a value of approximately 9.8 meters per second squared.

2. How is free fall acceleration used to find another acceleration?

Free fall acceleration can be used to find another acceleration by measuring the time it takes for an object to fall a certain distance, and then using the formula a = 2d/t^2, where a is the acceleration and d is the distance.

3. Can free fall acceleration be used to find any type of acceleration?

No, free fall acceleration can only be used to find the acceleration due to gravity. Other types of acceleration, such as centripetal acceleration, require different formulas and methods to calculate.

4. What are some real-life applications of using free fall acceleration to find another acceleration?

One common real-life application is in physics experiments or demonstrations, where free fall acceleration can be used to measure the acceleration due to gravity. It is also used in engineering and construction to calculate the acceleration of objects falling under the influence of gravity.

5. Are there any limitations to using free fall acceleration to find another acceleration?

Yes, there are some limitations. Free fall acceleration assumes that the object is falling in a vacuum, without any air resistance. In reality, most objects experience some resistance from the air, which can affect the accuracy of the calculation. Additionally, free fall acceleration can only be used for objects falling near the surface of the Earth, as the acceleration due to gravity varies at different altitudes.

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