how to write a function called kinematics to compute and plot the displacement of a particle falling under the influence of gravity, in matlab

Here is a possible implementation of the kinematics function which takes the initial velocity and the time interval as inputs, and returns the time and displacement vectors:

main.m
function [t, y] = kinematics(v0, dt, nsteps)
% Compute the displacement of a particle falling under the influence of gravity.
% Input arguments:
%   v0: initial velocity (m/s)
%   dt: time step (s)
%   nsteps: number of simulation steps
% Output arguments:
%   t: time vector (s)
%   y: displacement vector (m)

% Acceleration due to gravity
g = 9.81; % m/s^2

% Compute time and displacement vectors
t = linspace(0, nsteps*dt, nsteps+1)';
y = v0*t - 0.5*g*t.^2;

% Plot displacement vs. time
plot(t, y)
xlabel('Time (s)')
ylabel('Displacement (m)')
title('Kinematics of a falling object')
grid on

end
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You can call the function like this:

main.m
[t, y] = kinematics(0, 0.1, 100);
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This will simulate the motion of an object starting from rest (v0=0) with a time step of 0.1 seconds, and for a total of 100 steps (nsteps=100). The function returns the time and displacement vectors which can be plotted using the plot function.

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