Question

Solve and plot with MATLAB .

A safety bumper is placed at the end of a racetrack to stop out-of-control cars. The bumper is designed such that the force that the bumper applies to the car is a function of the velocity v and the displacement x of the front edge of the bumper according to the equation: where K = 30 (s kg)/m5 is a constant. A car with a mass m of 1,500 kg hits the bumper at a speed of 90 km/h. Determine and plot the velocity of the car as a function of its position for m. Hints: F=ma;vdv=adx

Answer 1

auelesation du a = dx fnet ma . - FC m. V dv Ta dr KV3 (1+x)3 = mv dv de ku? (1+x) > m

clc
clear all

syms v(x)

vi = 90*5/18; % initial velocity (m/s)
xi = 0; % initial position (m)
m = 1500; % mass (kg)
K = 30; % constant (kg-s/m^5)

%% Differential equation and initial condition
ODE = diff(v,x) == -K*v^2*(1+x)^3/m; % differential equation
cond = v(xi) == vi; % initial condition

%% solution of differential equation uisng dsolve function
v = dsolve(ODE,cond); % velocity as function of x

%% Array of values of velocity and position;
X = 0;
dX = 0.1;
V = [];
while 1
V(end+1) = double(subs(v,X(end)));
  
if V(end)<0.1
break
end
X(end+1) = X(end)+dX;
end
%% Plotting results
plot(X,V,'LineWidth',2);
xlabel('x (m)');
ylabel('v (m/s)');
title('Velocity as Function of Position');
xlim([X(1) X(end)]); Thank you...

Velocity as Function of Position 20 15 (s/w) 10 H 5 0 - x (m)