7, 100 + 20 = 120 points The following data were collected for distance traveled versus time for a rocket. Calculate the rocket's velocity and acceleration at each time using finite difference formula with error term O(h'); use the formulae for the finite difference approximations as given below. Note that you must have to use a forward difference approximation for the first data point, a backward difference formula for the last data point, and a centered difference scheme for the rest. -f(xi+2)4 f (xi+1) 3f(x) + O(h2) Forward Finite-difference: Backward Finite-difference: Centered Finite-difference : f'(xi) - f'(x) = f'(x) - 3 f(x) - 4 f(xi-1+f(x). 2 l + o(h2) 2 Ax 0 0 25 32 50 58 75 78 100 92 125 100 150 105 km Plot velocity and acceleration versus time graphs