Two cars A and B are travelling the same direction The cars

Two cars, A and B, are travelling the same direction. The cars are initially traveling 65 mph. Traffic ahead stops suddenly, and car A begins to decelerate at 1/3 g. After 2 s (normal recognition and reaction time), car B begins to decelerate at 2/3 g. Write a matlab code to accomplish the following:

Solution

intial velocity u = 65mph=95.3 ft/s

I did everything in code.

u = 95.3;% initial velocity
a1 = 10/3; % decceleration of car A, considered g=10
a2 = 20/3;
t = 0:0.01:6 % in seconds
t1 = u/a1; % Time for car A to stop
t2 = u/a2+2; %Time for car B to stop
%Both cars have same veloity at t = 0 and t1=28.6s and t2 = 14.3s
%Plot of Velocity of both the cars
v1 = u*t-a1*t;
v2 = u*(t)-a2*(t-2);
plot(t,v1);
hold on
plot(t,v2);
hold off

%Plot of Distance travelled
s1 = u*t-a1*t.^2/2; % Distance travelled by the car A
s2 = u*(t)-a2*(t-2).^2/2; % Distance travelled by the car B
plot(t,s1,\'r\');
hold on
plot(t,s2);
hold off
s = s1-s2;

plot(t,s); % Diffreence of distance with time
% in time t car A will move s1 distance And car B moves s2= u(t)-a2*(t-2)^2
% Distance need to avoid collision is s = s1-s2
d = (a1*t^2+a2*(t-2)^2)/2;
% so time at which it will collide is
T = (2*sqrt(a2)/(sqrt(a1)-sqrt(a2));

D = a2*2.5^2+a2*.5^2;
V = u*t-a1*t-v2 = u*2.5-a2*.5 % Differential speed