Skip to main content

A rabbit and a fox ran a race. They started in the same direction, from the same place. The rabbit accelerated 5.0m/s2 up to its maximum speed. It...

To determine the distance traveled by the rabbit in 8 seconds, let's divide it into two time intervals. The time intervals are from 0 to 4 seconds and from 4 to 8 seconds.


At time interval from t=0s to t=4s, the rabbit starts from rest and has a constant acceleration of 5m/s^2. Applying the formula


`d= v_i Delta t + 1/2a Delta t ^2`


it traveled a distance of


`d_(R1) = 0 + 1/2 (5)(4)^2`  


`d_(R1) = 40`  meters


Next, applying the formula


`v_f = v_i + a Delta t`


the maximum speed of the rabbit is:


`v_(R) = 0 + 5*4`


`v_(R) = 20` m/s


At the time interval from t=4s to t=8s, the rabbit is running at a constant speed v_(R). So, its acceleration is zero. It has traveled a distance of


`d_(R2) = v_(R) Delta t +1/2a Delta t^2`


`d_(R2) = 20 * 4 + 0`


`d_(R2) = 80m`


Hence, the rabbit has traveled a total distance of


`d_R= d_(R1) + d_(R2)`


`d_R = 40 + 80`


`d_R = 120 m`



To determine the distance traveled by the fox, apply the formula:


`d= v_i Delta t + 1/2at^2`


Since the fox starts from rest and accelerates at 2 m/s^2, the distance traveled from t=0s to t=8s is:


`d_F = 0 + 1/2*2 * 8^2`


`d_F = 64` meters


The distance between the rabbit and the fox at t=8s is:


`d = d_R - d_f`


`d = 120 - 64`


`d=56 m`


Therefore, at t=8s, the rabbit is ahead by 56 meters.

Comments

Post a Comment

Popular posts from this blog

Is there a word/phrase for "unperformant"?

As a software engineer, I need to sometimes describe a piece of code as something that lacks performance or was not written with performance in mind. Example: This kind of coding style leads to unmaintainable and unperformant code. Based on my Google searches, this isn't a real word. What is the correct way to describe this? EDIT My usage of "performance" here is in regard to speed and efficiency. For example, the better the performance of code the faster the application runs. My question and example target the negative definition, which is in reference to preventing inefficient coding practices. Answer This kind of coding style leads to unmaintainable and unperformant code. In my opinion, reads more easily as: This coding style leads to unmaintainable and poorly performing code. The key to well-written documentation and reports lies in ease of understanding. Adding poorly understood words such as performant decreases that ease. In addressing the use of such a poorly ...
Post a Comment
Read more

A man has a garden measuring 84 meters by 56 meters. He divides it into the minimum number of square plots. What is the length of the square plots?

We wish to divide this man's garden into the minimum number of square plots possible. A square has all four sides with the same length.Our garden is a rectangle, so the answer is clearly not 1 square plot. If we choose the wrong length for our squares, we may end up with missing holes or we may not be able to fit our squares inside the garden. So we have 84 meters in one direction and 56 meters in the other direction. When we start dividing the garden in square plots, we are "filling" those lengths in their respective directions. At each direction, there must be an integer number of squares (otherwise, we get holes or we leave the garden), so that all the square plots fill up the garden nicely. Thus, our job here is to find the greatest common divisor of 84 and 56. For this, we prime factor both of them: `56 = 2*2*2*7` `84 = 2*2*3*7` We can see that the prime factors and multiplicities in common are `2*2*7 = 28` . This is the desired length of the square plots. If you wi...
Post a Comment
Read more