Question

The curvilinear motion of a particle is defined by the following parametric equations

𝑥 = 52𝑡 − 9𝑡

2

, 𝑦 = 125 − 5𝑡

3

The velocity of a particle is defined by 𝑣 = √𝑣𝑥

2 + 𝑣𝑦

2. For time interval [0 6] make a first

plot that shows the position of the particle ( y vs x) and a second plot ( on the same figure 

window) of the velocity of the particle as a function of time. In addition, using an asterisk 

marker show the position of the particle ( in first plot ) at which its speed is maximum. For time 

use a vector with spacing of 0.1s.

Answer 1

close all,
clear all,
clc,


syms t
x = 52*t - 9*t^2;
y = 125 - 5*t^3;
Vx = diff(x);
Vy = diff(y);
v = sqrt(Vx^2 + Vy^2);


t = 0:0.1:6;
X = subs(x,t);
Y = subs(y,t);
scrsz = get(0,'ScreenSize');
Dim=0;
figure('Position',[scrsz(1)+Dim, scrsz(2)+Dim,scrsz(3)-20,scrsz(4)-100]);
subplot(2,1,1);
plot(X,Y,'o'); hold on
plot(X,Y,'-');
grid on,
xlabel('--- x --->');
ylabel('--- y --->');
title('Position Plot: X-Y','FontSize',20);
hold on,
V = subs(v,t);
subplot(2,1,2);
plot(t,V);
grid on,
xlabel('--- t --->');
ylabel('--- Velocity --->');
title('Velocity Plot','FontSize',20);