Super fast average acceleration confusion problem

In summary, the car's average acceleration during the interval of time is 20^2/r to the north, with a magnitude of 20^2/r and a direction of north. This is found by using the formula a= v2-v2/t and using a motion diagram to determine the direction. The length of the arc can be found using the kinematic equation d(final)=v(initial)T, and by multiplying it by four, the circumference can be found. Plugging in the value for the radius into the formula 20^2/r gives the magnitude of the car's average acceleration. The direction can be determined by averaging out the directions of the tangent lines at 45 degrees from both the northwest and northeast, resulting in a
  • #1
sarahaha288
17
0

Homework Statement



a car traveling at a constant speed of 20 m/s that is initially traveling due northwast rounds a corner so that after 10s, the car is traveling due northeast. What are the magnitude and direction of the car's average acceleration during this interval of time?

Homework Equations



a= v2-v2/t

The Attempt at a Solution


i divided 20m/s/10s and got 2 m/s and used a motion diagram to get the direction to be northward. This is not right. I'm not sure how to do it because it is a constant speed, so wouldn't the velocity be -20-20/10? and that would definitely be 0, and the acceleration is not 0 becasue it is chaning direction.
 
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  • #2
The car's changing directions, so you have to find the vector representing the change in velocity. Draw a vector diagram of the car's velocity to see what's going on.
 
  • #3
ok so for your average acceleration is just 20^2/radius which is going to be your magnitude. in order to find the radius you need to find the length of the arc. And because the car is traveling at a uniform speed you can just use a simple kinematic equation to find the arc distance. d(final)=d(initial) +v(initial)*T+(aT^2)/2 which in this case is shortend to d(final)=v(initial)T. that is 1/4 of your circle so multiply that by four. That is now your circumference. So C=2[tex]\pi[/tex]r. plug in your answer for r into 20^2/r and you have your magnitude. To find the direction is much more simple. If you were to lay that part of a curve on a grid, say from Y at 1 to X at 1 and you draw say 9 total tangent lines. all of their directions will average out to be the same direction the tangent line that is at 45 degrees. So 45 degrees from both the northwest and the northeast leaves you with a direction of north.
Final answer: 20^2/r to the north
 

What is the "Super fast average acceleration confusion problem"?

The "Super fast average acceleration confusion problem" is a common issue encountered by scientists and engineers when calculating the average acceleration of an object over a short time interval. It occurs when there is a large difference between the initial and final velocities of the object, causing the average acceleration to appear much higher than expected.

What causes the "Super fast average acceleration confusion problem"?

This problem is caused by the inconsistency between the average acceleration and the instantaneous acceleration of an object. Average acceleration is calculated by dividing the change in velocity by the change in time, while instantaneous acceleration is the acceleration at a specific moment in time. When there is a large difference between the initial and final velocities, it can lead to a significant discrepancy between the two values.

How does the "Super fast average acceleration confusion problem" affect scientific experiments?

The "Super fast average acceleration confusion problem" can affect the accuracy of scientific experiments, especially those involving calculations of average acceleration. It can lead to incorrect conclusions and misleading data if not properly addressed.

What are some ways to avoid the "Super fast average acceleration confusion problem"?

To avoid this problem, scientists and engineers can use smaller time intervals when calculating average acceleration, or they can use more precise methods to measure instantaneous acceleration. Another approach is to take multiple measurements and calculate the average of those values, which can help to minimize the impact of any outliers.

Can the "Super fast average acceleration confusion problem" be completely eliminated?

No, this problem cannot be completely eliminated, as it is a natural result of the differences between average and instantaneous acceleration. However, by using appropriate methods and techniques, its impact can be minimized and managed effectively in scientific experiments.

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