function [x,v] = falling_object(g,m,k,t)
% A function to calculate the position and velocity of
% a falling object with air resistance proportional to velocity.
% It is assumed that the initial position is 0 with positive
% direction downward and that the initial velocity is also 0
%
% Input:
%   g: the acceleration due to gravity (for example 9.81 m/s^2)
%   m: the mass of the object (for example, 10 kg)
%   k: the drag coefficient (for example, 2 kg/s
%   t: the time in seconds since object was dropped
% Output:
%   x: the position at time t
%   v: the velocity at time t

c1 = m*g/k;
c2 = m/k;

% Initial conditions at time 0 

x0 = 0;
v0 = 0;

% Formulas for velocity and position aat time t

v = c1 + (v0 - c1)*exp(-t/c2);
x = x0 + c1*t + c2*(v0 - c1)*(1 - exp(-t/c2));
end