The following data was collected for the distance traveled versus time for a rocket: t, s 0 15 30 45 60 75 y, km 0 1.69 7.19 17.2 32.3 53.3 Use numerical differentiation to estimate the vertical component of the rocket’s velocity and acceleration at t = 0, t = 30, and t = 60 seconds. At each time, use the least computationally expensive algorithm with an O(h4 ) error. The numerical differentiation formulae can be found on the equation sheet.

Two kilograms of air within a piston–cylinder assembly executes a carnot power cycle with maximum and minimum temperatures of 800 k and 300 k, respectively. the heat transfer to the air during the isothermal expansion is 60 kj. at the end of the isothermal expansion the volume is 0.4 m3. assume the ideal gas model for the air. determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kj.