I am driving my 1,500 kg car along at 21 m/s. I take my foot off the accelerator

Question

I am driving my 1,500 kg car along at 21 m/s. I take my foot off the accelerator and apply the brakes, which provide a stopping force of 4,500 N. 6. Provide a set of equations I need to numerically integrate if I want to find the position of the car at any given time. 7. Using numerical integration (At- 1s with either a left or right hand Riemann sum) in an Excel or Libre Office spreadsheet, give the acceleration, velocity, and position of my car until it comes to a stop. 8. Change the timestep for numerical integration to O.1s. Does this change in timestep change our solution for how far the car traveled before stopping? 9. How might the problem of timesteps affect a molecular dynamics simulation? What are the advantages and disadvantages of a long and a short integration timestep?

Explanation / Answer

6. a = F/m = 4500/1500 = 3

Now distance = (Vf^2 - V20)/2a = 21^2 / 2*3 = 141/6 = 23.5m

s= ut +1/2at^2 = 21t + 3/2 t^2

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