Piecewise does not translate properly

  • Thread starter dumguy
  • Start date
In summary, a car traveling at a constant velocity of 18 m/s is 40 metres away from a school bus when the driver sees the stop sign. The driver has a reaction time of 0.75 seconds and after the brakes are applied, it takes 3 seconds for the car to come to a stop. A piecewise-defined function can be used to describe the distance traveled by the car until it stops, with one equation for the time before the reaction time and one for after. However, there are inconsistencies in the given information, such as the contradictory initial velocities in the two equations, and therefore different methods may result in different answers. Further investigation and clarification is needed to accurately determine the distance traveled by the car before it stops
  • #1
dumguy
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0
1. Homework Statement [/b]A car is driving at a constant velocity of 18 m/s. There is a school bus on the road with its stop sign extended. The car is 40 metres away from the bus when the driver sees the stop sign.
There is a time delay of 0.75 secondsbetween the time the driver sees the sign and when the driver can begin to slow down. This is called the "driver reaction time". During this reaction time the distance d, in m, traveled by the car is given by the equation d=18t, where t is the time in seconds from when the driver sees the bus. When brakes are applied, after the 0.75 second reaction time, the distance d traveled by the car in time t is given by the equation d=-3t^2+22.5t-1.6875. After the brakes are applied it takes 3 seconds for the car to come to a stop. These 3 seconds plus the 0.75 second driver reaction time means the car stops 3.75 seconds after seeing the school bus.
i) Write a piecewise-defined function to describe the distance traveled by the car until it stops.iv)how far does the car travel befor it stops?Explain how you found this.

d=(18t, 0<=t<=0.75
(-3t^2+22.5t-1.6875, 0.75<t<=3.75

When I solve the equations individually and add them together, I get 13.5+38.8125=53.3125
When I graph the piecewise on graphing calculator, I get a graph with an end coordinate of
(3.75, 40.5). How is this possible and which one is correct?
 
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  • #2
I don't know anything about the graphing solution, but there is something odd about this problem. The formula d=18t says that the initial speed is 18 m/s. But the second term of d=-3t^2+22.5t-1.6875 says that the initial velocity is 22.5 m/s, a contradiction. The -1.6875 doesn't make any sense. If you use the acceleration of -3 from an initial speed of 22.5, you get a deceleration time of 7.5 s, not 3 s. The question has conflicts in it so it is not surprising that different methods result in different answers.
 
  • #3
perhaps if i translate the parabola up 13.5 units and right 0.75 units we can get a better result. Something is lost in the translation from 2 individual functions to a piecewise. Any ideas are welcome and appreciated.
 

What does it mean when it says "Piecewise does not translate properly"?

When a computer program or mathematical software displays the message "Piecewise does not translate properly," it means that the program is unable to interpret or understand a piecewise function that has been entered. This could be due to incorrect syntax, missing information, or other errors within the function.

Why is it important to ensure that piecewise functions translate properly?

Piecewise functions are commonly used in mathematics and scientific research to model complex relationships and solve problems. If the function does not translate properly, it may produce incorrect results or cause errors in the calculations, leading to inaccurate conclusions.

What are some common errors that can cause piecewise functions to not translate properly?

Some common errors that can prevent piecewise functions from translating properly include missing parentheses, incorrect placement of brackets, missing or incorrect variables, and missing or incorrect mathematical operators. It is important to double-check the syntax and format of the function to ensure it is entered correctly.

How can I troubleshoot and fix issues with piecewise functions not translating properly?

If you encounter errors with piecewise functions not translating properly, the first step is to carefully review the function and check for any syntax or formatting errors. If the function appears to be correct, try breaking down the function into smaller pieces and testing each piece separately. This can help identify where the error is occurring. Additionally, consulting a programming or mathematics expert may also be helpful in troubleshooting and fixing the issue.

Are there any best practices to follow when working with piecewise functions to avoid translation errors?

To avoid translation errors, it is important to follow proper syntax and formatting guidelines for piecewise functions. This may include using parentheses and brackets correctly, using clear and consistent variable names, and avoiding common mathematical errors. Additionally, it is helpful to break down complex functions into smaller pieces and test each piece separately before combining them into a larger function.

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