i want solve this question by matlab code The upward velocity of a rocket is giv

Question

i want solve this question by matlab code

The upward velocity of a rocket is given as a function of time in Table 1. Determine the value of the velocity at t = 16 seconds by using Newton's divided difference polynomial method Table 1 Velocity as a function of time. Newton's Finite Difference Algorithm: INPUT numbers x_0, x_1, ..., x_n; values f (x_0), f(x_1), ..., f(x_n) as F_0.0, F_1, 0, ....., F-n, 0. OUTPUT the numbers F_0, 0, F_1, 1.....F-n, n where P_n(x) = F_0, 0 + sigma^n _i = 1 F_i, j PI^I = 1 _j = 0 (x - X_j).(F_i, I is f[x_0, x_1....., x_i].) Step 1 For i = 1, 2, ...., n For j = 1.2, ..., I set F_i, J = F_ij-1 - F_i-1j-1/x_i - x_i - j. (F_i, j = f[x_i-j, ....., x_i].) Step 2 OUTPUT (F_0.0, F_1, 1, ..., F_n, n); STOP.

Explanation / Answer

Programme::

time = [0 10 15 20 22.5 30]; %create time matrix from time data given
velocity = [0 227.04 362.78 517.35 602.97 901.67]; %create the velocity matrix corresponding to time matrix
t = 16;%define the time at which velocity has to be found
diff = [];
for i = 1:length(time)
if time(i) <= t
new = t-time(i);
diff = [diff new];
end
end
[m, I] = min(diff,[],2);
t_low = time(I); %lower limit here it is 15 seconds
v_low = velocity(I); %velocity at time t_low
t_up = time(I+1);%upper limit here it is 20 seconds
v_up = velocity(I+1); %velocity at time t_up
v = v_low + (v_up-v_low)*(t-t_low)/(t_up-t_low);
disp('the velocity at required time in m/s is = ')
disp(v)

Output::

the velocity at required time in m/s is =
393.6940

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