PHYS 4A Non-Constant acceleration Activity

Purpose: In this lab we are depict a 5000 Kg elephant with a rocket strapped to its back and try to determine how far the elephant goes before it stops. The rocket provides a constant 8000 N Force and burns fuel at a rate of 20 kg/s so it mass changes according to the following equation m(t) = 1500-20t.

We start off with or acceleration function

 After we integrate the acceleration function, we get our velocity function below
 And finally, we integrate for a third time and we get our position function below.

The data set below depicts all three functions. The highlighted portions on both spread sheets represent the time, distance and velocity of the elephant when it changes direction of motion. The picture below shows a time interval of 0.05 seconds difference and we show a total horizontal distance of 248.67m

The image below is similar but shows a time interval change of .10 seconds. Horizontal distance remains the same as well as the time elapsed to slow down and change direction

Conclusion: After we solved for all the functions and used Excel to plot our data, we showed that the time needed to stop the elephant was 19.69 s and the distance the elephant had traveled equated to 248.7 m. We were able to get very precise with our numbers by changing the time interval to different amounts and finding where out velocity would be equal to 0. In our case, it turns out to be around 19.6 seconds. We chose these intervals because they gave us the closest amout to 0 as we could get without getting to extreme on our precision.