Lab $2$: Algorithms

Overview:

As we have learned in class, for each problem, we can come up with a solution algorithm. In any algorithm, we

should determine the problem statement, the inputs$($knowns$),$ the outputs $($unknowns$),$ and the algorithm

assumptions. Developing correct and efficient algorithms is very important in engineering problems. This lab

will allow students to practice algorithm development and writing MATLAB live scripts.

Learning Objectives:

Practice algorithm development.

Demonstrate proficiency coding algorithms in MATLAB.

Problem Description

The problem under investigation is motion in a straight line under constant acceleration kinematics problem.

The motion equations are given as follows.

$(1)x=x_0+v_{0}t+\frac{1}{2}a{t}^2$

$(2)v=v_0+at$

$(3)v^2=v_0^2+2a(x-x_0)$

where Given $0($m$/$s$),0($m$/$s$)$ and a $($m$/$s$^2)$ as input from users, you are required to calculate the following:

a$)$ The distance travelled at time of interest, t $=3$ seconds in $($ft$)?$

b$)$ The velocity after time of interest, t$=3$ seconds, in $($ft$/$s$)?$

c$)$ The distance to reach a velocity of interest v$=10$ m$/$s$?$

d$)$ The time to reach a velocity of interest v$=10$ m$/$s$?$

Hint: your formulas need to be adjusted for $($c$)$ and $($d$)$

Lab Report

You will submit a report of your work via Blackboard in a single usable live script MATLAB file. Make sure to

include $($and label$)$ the following information.

I. Abstract $$ In $3-5$ sentences summarize what your code is doing, and how someone unfamiliar with

MATLAB could use it$.$

II$.$ Algorithm $$ Write out the steps performed by your code. You may use a list of steps in the algorithm

or import a graphical algorithm.

III. Code $$ Separate your code into sections defined by each step in the Laboratory Procedure

a$.$ Gathering user inputs

b$.$ Performing calculation

c$.$ Making necessary conversions

d$.$ Outputting the results

Questions $$ answer the following questions after the end of your code.

a$.$ What is the formula needed to calculate the distance from velocity?

b$.$ What is the formula needed to calculate the time from velocity?

c$.$ What are the unit conversions used in the lab.

V$.$ Bonus $($Optional$)$ Modify your code to plot the relation between $($t$,$x$)$ and $($t$,$v$)$ for t $=0$:$0\mathrm{.}1$:$10.$ A

sample figure is shown below

VI$.$ Student Questions $($Optional$)$ This is a space for you to list any lingering questions you may have about the lab