Air track question...maximum possible value?

Question

what is the maximum possible value of the slope of a v versus t curve for a car released from rest on an air track elevated on one end

Answer 1

The maximum according to theory is infinity.

As infinity is impossible to achieve the max slope is 5.72 * 10 power 10.

Answer 2

Acceleration is the derivative of "v vs. t", so that means that the slope of the "v vs. t" curve is acceleration itself.  On earth, the acceleration due to gravity is 9.8 m/s², so your car cannot exceed that acceleration when released.

Thus, assuming you are on Earth, and your chart is in seconds and meters, then the maximum "v vs. t" slope (acceleration) you can have is 9.8.

Answer 3

The slope of a V vs t curve is the acceleration.  So, the max slope is the only thing pulling on the car, which is gravity, g =9.8m/s^2