I get two different answers when solving a kinematics problem

In summary: Is a non-constant acceleration "inherently flawed" in your opinion? In any case, the problem is asking for the acceleration, which is ##\frac{dv}{dt}##, and not for the average acceleration, which is ##\frac{\Delta v}{\Delta t}##.
  • #1
LugubriuousLamia
10
3
1. A car accelerates for 200 meters and has an initial velocity of 2.0 m/s and a final velocity of 6 m/s. What is the acceleration of the car if this change in velocity takes 12 seconds?

Homework Equations


a=Δv/Δt
Δx=Vi*t+.5at2[/B]

The Attempt at a Solution


When I solve this using the first equation I get the acceleration is equal to .33 m/s2 because (6m/s - 2m/s)/ 12 seconds = .33 m/s2

However when I use Δx=Vi*t+.5at2 I get[/B]

200m= 2m/s*12 sec+.5*a*12 sec2
With a being equal to 2.4 m/s2

Which of these answers would be the correct answer to this problem. I am inclined to believe that the correct answer would be the first answer. However I am not sure as to why this would be the case. I am looking for a concrete reason as to why one solution would be more correct than the other.
 
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  • #2
Assuming that the acceleration is constant, your results show that the assumptions on the distance, velocities, and time are incompatible. Note that (12 s)(6 m/s) = 72 m so even if the car was moving at the listed final speed for all of the 12 s, it would not reach a distance of 200 m.
 
  • #3
The only thing I can see is that the equation based on ##\Delta x## assumes that acceleration is constant, which is not specified in the problem. The best you can do is to calculate the average acceleration, using ##\Delta v / \Delta t##.

Edit: beaten by @Orodruin
 
  • #4
John Mantia said:
1. A car accelerates for 200 meters and has an initial velocity of 2.0 m/s and a final velocity of 6 m/s. What is the acceleration of the car if this change in velocity takes 12 seconds?

For future reference: if you have uniform acceleration from ##2m/s## to ##6m/s##, then the average velocity during this time is ##4m/s##.

And, if the time for this acceleration is ##12s##, then the displacement during this time is ##\Delta x = (4m/s)12s = 48m##.

Note: In general, the average velocity is ##\frac12 (v_i + v_f)## (assuming constant acceleration). Which is, in fact, half way between the two.

Also, if a car travels ##200m## in ##12s##, then its average velocity during this time is ##16.7m/s##, which is significantly greater than the speeds involved in your question.

Using average velocity is perhaps a good way to get a bit more intuition about the sort of numbers you expect in answer to these questions.
 
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  • #5
Thank you for the replies, it would seem that the problem is inherently flawed so there is no actual answer than can be obtained.
 
  • #6
That depends on your definition of "inherently flawed". I could certainly produce an acceleration profile that satisfies the given data, but it will not be a motion with constant acceleration.
 
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Related to I get two different answers when solving a kinematics problem

1. Why am I getting two different answers when solving a kinematics problem?

There could be several reasons for this. One possibility is that you made a mistake in your calculations. Double check your work to make sure all of your equations and values are correct. Another possibility is that there are multiple solutions to the problem, and you may have missed one. Lastly, it's possible that the problem itself is flawed or ambiguous, leading to multiple valid answers.

2. How do I know which answer is correct?

If you are confident in your calculations and have double checked your work, the best way to determine which answer is correct is to compare it to other known values or use common sense. For example, if your answer is a velocity that is greater than the speed of light, it is likely incorrect. Additionally, if the problem involves a physical scenario, you can use your understanding of the situation to determine if the answer makes sense.

3. Can both answers be correct?

In some cases, yes. As mentioned earlier, there may be multiple solutions to a kinematics problem. This could occur if there are multiple possible starting or ending points, or if there are multiple paths that an object could take to reach a certain point. It's important to carefully consider the problem and use logic to determine if both answers could be valid.

4. How can I avoid getting two different answers in the future?

To minimize the chances of getting two different answers, it's important to be thorough and organized in your problem-solving process. Clearly label and organize your equations and values, and double check your work along the way. It's also helpful to have someone else review your work and calculations to catch any mistakes or potential issues.

5. Is it normal to get two different answers when solving a kinematics problem?

While it's not uncommon to get two different answers, it shouldn't be the norm. With careful and thorough problem-solving techniques, it is possible to arrive at a single correct answer. If you consistently encounter multiple answers, it may be helpful to review your understanding of kinematics concepts and equations, and practice problem-solving techniques.

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