Question

Please show answer using MATLAB

Time, t(s)	0	2	4	6	8	10	12	14	16
Position, x(m)	0	0.7	1.8	3.4	5.1	6.3	7.3	8.0	8.4

1. To find the velocity at all times using the two-point differencing formula (and where appropriate the three-point forward or backward differencing formulae), these should yield the results correct to O(h²)
2. To find the acceleration at all times using the three-point central differencing formula (and where appropriate the four-point forward or backward differencing formulae), these should also yield the results correct to O(h²)
3. Plot the position, velocity and acceleration with respect to time

Answer 1

t = 0:2:16;
pos = [0 0.7 1.8 3.4 5.1 6.3 7.3 8.0 8.4];
vel = [];
acc = [];

for i = 1:length(t)-1
   vel(i) = (pos(i+1) - pos(i))/(t(i+1) - t(i));
end

for i = 1:length(t)-2
   acc(i) = (pos(i+2) - pos(i))/(t(i+2) - t(i));
end

subplot 311
plot(t,pos);
title("Plot of Position with time");
xlabel("t");
ylabel("x(t)");
subplot 312
plot(t(1:length(vel)),vel);
title("Plot of Velocity with time");
xlabel("t");
ylabel("v(t)");
subplot 313
plot(t(1:length(acc)),acc);
title("Plot of Acceleration with time");
xlabel("t");
ylabel("a(t)");