Question

1.Write down the fplot( ) command used to generate a straight line formed by two (x, y) points: (-3, 5) and (3, 8). Plot the line from -5 ≤ x ≤ 5. Show your derivation of the line equation.

2. [15pts] The position x as a function of time of a particle that moves along a straight line is given by

a. [3pts] Derive the expressions for the velocity and acceleration of the particle

Make plots of the position, velocity, and acceleration as a functions of time for 0 ≤ t ≤ 15 sec following the instructions below.

b. [6pts] Using plot( ), plot the position, velocity, and acceleration on a single plot window using black solid line, green dash line, and yellow dash-dot line, respectively. Show the plot in Figure 1. Use the line width of 2. Include the following title in bold face: “Motion profile of a particle between 0 ≤ t ≤ 15 sec”. Include proper legend and axis labels with units. Show grid lines. All formatting must be done inside your code and not from the Figure Editor.

c. [6pts] Using subplot, plot the position, velocity, and acceleration vs time in 3 separate plots arranged in a single column. Show the subplot in Figure 2. Include the following title in bold face above the top-most plot: “Position, velocity and acceleration profile of a particle”. Show grid lines and proper axis labels on all your plots. All formatting must be done inside your code and not from the Figure Editor.

Answer 1

The two points are given by (-3,5) and (3,8)

The equation of line joining two points is given by y-y1=(y2-y1)/(x2-x1)*(x-x1)

=> y-5=(8-5)/(3+3)*(x+3)

=> 2y-10=x+3

=> y=(x+13)/2 (Our Line Equation)

Using the command fplot(@(x) (x+13)/2), I got the following plot

Here suppose x is taken as time and y is taken as position of particle

rewriting this equation in terms of position and time, we get

x=(t+13)/2;

The velocity of a particle is the differentiation of position with respect to time

=> we get velocity v=dx/dt=1/2;

the acceleratio of a particle is the differentiatio of velocity with respect to time

=> we get acceleration a=dv/dt=0;

plotting position, velocity and acceleraton with respect to time in MATLAB, we get

and the Matlab code is

clc
clear
t = linspace(0,15);
x=(t+13)/2;
v=1/2+0*t;
a=0+0*t;
plot(t,x,'-k','LineWidth',2,'markerfacecolor','k');
    hold on
    plot(t,v,'--g','LineWidth',2,'markerfacecolor','g');
    hold on
    plot(t,a,'-.y','LineWidth',2,'markerfacecolor','y');
    axis on;
    grid on;
    title('\fontsize{16}\fontname{Times New Roman}Motion profile of a particle between 0<=t<=15 sec');
    xlabel('\fontsize{12}\fontname{Times New Roman}time(sec)');
    ylabel('\fontsize{12}\fontname{Times New Roman}position(m) velocity(m/s) acceleration(m/s^2)');
    legend('position','velocity', 'acceleration');
    axis([0 15 0 inf]);

Using subplot, I got the following figure

and the Matlab code is

clc
clear
title('Position, velocity and acceleration profile of a particle')
subplot(3,1,1)
t = linspace(0,15);
x=(t+13)/2;
plot(t,x,'-k','LineWidth',2,'markerfacecolor','k');
axis on;
grid on;
title('\fontsize{12}\fontname{Times New Roman}"Position, velocity and acceleration profile of a particle”');
xlabel('\fontsize{12}\fontname{Times New Roman}time(sec)');
ylabel('\fontsize{12}\fontname{Times New Roman}position(m)');

subplot(3,1,2)
t = linspace(0,15);
v=1/2+0*t;
plot(t,v,'--g','LineWidth',2,'markerfacecolor','g');
axis on;
grid on;
xlabel('\fontsize{12}\fontname{Times New Roman}time(sec)');
ylabel('\fontsize{12}\fontname{Times New Roman}velocity(m/s)');

subplot(3,1,3)
t = linspace(0,15);
a=0+0*t;
plot(t,a,'-.y','LineWidth',2,'markerfacecolor','y');
    axis on;
    grid on;
xlabel('\fontsize{12}\fontname{Times New Roman}time(sec)');
ylabel('\fontsize{12}\fontname{Times New Roman}acceleration(m/s^2)');