6. 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(x+2)+4 f(x1+1) - 3 f(x1) Forward Finite-difference: f'(x) = Backward Finite-difference: f'(x) = Centered Finite-difference : f'(x)= + O(h) 2 Ax 3 f(x)-4 f(x-1) + f(x1-2) + O(h) 2 Ax f(x1+1)f(x-1) + O(h) t, s y, km 0 25 50 75 100 125 150 0 32 58 78 92 100 105 Plot velocity and acceleration versus time graphs. 2 Ax