Acceleration from min/max derivatives

[Turtlie]

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.

 

[tiny-tim]

Hello Turtlie

(try using the X² icon just above the Reply box )

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 ? ​

 

[Turtlie]

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.

 

[SammyS]

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?

 

[tiny-tim]

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?