Acceleration from min/max derivatives

AI Thread Summary
The discussion centers on finding acceleration from the min/max derivatives of the function x(t) = -0.01t^3 + t^2 - 20t + 4. The derivative calculated is -0.03t^2 + 2t - 20, with critical points identified at t = 12.3 and t = 54.4, yielding positions of -100 and 250, respectively. A secondary question involves determining the optimal time to wind a flywheel for a car to cover 100 meters with a constant acceleration of 0.5 m/s². The participants express confusion about the calculations and discuss the strategy of balancing winding time with cruising speed. The thread highlights the complexities of motion equations and optimization in physics problems.
Turtlie
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Homework Statement


x(t) = -0.01t^3 + t^2 - 20t + 4


Homework Equations


Min is when t = 12.3
Max is when t = 54.4


The Attempt at a Solution


I got -0.03t^2 + 2t - 20 as the derivative.
I substituted in t = 12.3 and 54.4 and got 0.02 and 0.19 which don't seem right at all.
Because: when t is 12.3, the position(x) is -100. When t is 54.4 the position(x) is 250.
 
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Hello Turtlie :smile:

(try using the X2 icon just above the Reply box :wink:)
Turtlie said:
I got -0.03t^2 + 2t - 20 as the derivative.
I substituted in t = 12.3 and 54.4 and got 0.02 and 0.19 which don't seem right at all.

Well, to only 3 https://www.physicsforums.com/library.php?do=view_item&itemid=523" that looks acceptably near zero …

what happens if you solve that quadratic equation to 4 sig figs ? :smile:​
 
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Ah looks like I was right then, and thank you for the hint ;)

I've got another question.
A flywheel car is capable of giving a car a constant acceleration of 0.5m/s2, but only for as long as it is wound up for (if it is wound up for 5 seconds it will accelerate at 0.5m/s2. Once the flywheel is finished unwinding it will continue rolling at a constant velocity.

How long should you spend turning the flywheel if the length of the race is 100 meters. The time spent turning the flywheel counts towards the total time.

Honestly I'm completely stuck on this.
 
Turtlie said:
Ah looks like I was right then, and thank you for the hint ;)

I've got another question.
A flywheel car is capable of giving a car a constant acceleration of 0.5m/s2, but only for as long as it is wound up for (if it is wound up for 5 seconds it will accelerate at 0.5m/s2. Once the flywheel is finished unwinding it will continue rolling at a constant velocity.

How long should you spend turning the flywheel if the length of the race is 100 meters. The time spent turning the flywheel counts towards the total time.

Honestly I'm completely stuck on this.

At a constant acceleration of 0.5m/s2, how long will it take the car to go 100m, if it starts from rest?
 
SammyS said:
At a constant acceleration of 0.5m/s2, how long will it take the car to go 100m, if it starts from rest?

ah, but maybe it's better to spend less time winding it, and to let it cruise for the last 10 m or so? :smile:
 

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