We are given the following data for the velocity as a function of time: 20 227.04 362.78 517.35 602.97 901.67 10 30 t(s) v(t) (m/s) 15 22.5 (1) Determine the value of the velocity at t=16 s using...

Extracted text: We are given the following data for the velocity as a function of time: 20 227.04 362.78 517.35 602.97 901.67 10 30 t(s) v(t) (m/s) 15 22.5 (1) Determine the value of the velocity at t=16 s using third order Lagrangian polynomial interpolation. (2) Find the absolute relative approximate error for the third order polynomial approximation, if v(16) = 392.19 m/s using the second order polynomial. (3)Using the third order polynomial interpolant for velocity, find the distance covered from t-11 s to t=16 s. (4) Using the third order polynomial interpolant for velocity, find the acceleration at t=16 s.