Before we start, I want to mention that I normally use a default template that my college professor gave me (which I did modify to suit my needs of course) and use that in pretty much all my problem solving in MathCAD. If you wish to follow along on this tutorial using the same template, the file is available here.

In this small tutorial I will teach you how to use MathCAD in solving uniform acceleration problems. This tutorial will cover the basics of units, functions, ranges and arrays in MathCAD along with shading and decimal formatting. So say we are given the following problem:

Skipper is driving at an initial velocity of Vo. The car travels at a speed of a. Compute the distance X traveled and the speed V of an accelerated object.

How would you go about approaching this problem? What should you do first in MathCAD? Well that’s simple, we always start of by adding a title to our document. On the top left of MathCAD ribbon, you will see a drop-box that presents us with several styles. Select the header text and from the drop-box select “Heading 1.” This will transform our simple style to a heading style. Next lets add the problem statement (see above).

In reality we are always greeted with friction. Friction is a resistive force that is relative to motion. For now we are going to assume that our situation of Skipper is driving in perfect condition where friction does not exist. With that said, lets write down our equations of motion:

X=V_o t+1/2 at^2
V=V_o+at

Mathcad: In MathCAD if you wish to make a subscript, you can either use the dashboard options or simply add an period like so: V.o . For superscript we use a carrot ^ like so: t^2. For the equal sign we are going to be using a symbolic (Boolean) equal sign created by holding CTRL and hitting the “=” key.

These are two very useful and required formula in solving this problem. However, we don’t have any values to plug and chug. Without any values, this problem is un-solvable. So lets say we were told that
Acceleration: a=3.5 m/s^2
Initial Velocity: V_o=12 mph

Now the equation is helpful to us. But before we continue, we need convert our original equations into functions (functions of time f(t)). We do this because the distance traveled is based on how much time has passed.

X(t)=V_o t+1/2 at^2
V(t)=V_o+at

MathCAD: Note the distance and velocity equations copied from above and “=” changed to an ‘assignment’ equal “:=”. In MathCAD if you don’t have a previously defined formula, the equal sign that you use will change to an assignment equal. Note: the green ‘wavy’ line indicates that a variable name has been redefined (in this case V is Mathcad default for volt units).

To solve this problem, we first need to solve for the velocity. We are going to do this by using a time range to calculate a series of points. For us lets say the range for time is between 0s to 10s (where s is seconds).

t=0s,1s..10s

MathCAD: Since we are working with units, units must be supplied with each value in the range. 1st value of t = 0 seconds, 2nd value of t = 2 seconds, last value = 10 seconds. The “..” is generated by a semicolon “;”

We now want to display out results in a matrix. MathCAD already has a built in function that can do the dirty work for us. To do this, we click on Format > Results from the main menu. There click on the “Display Options” tab and from the matrix display style drop-box select Matrix.

Now in MathCAD lets hit t and =. This should output a matrix containing even numbers ranging from 0 to 10 (see attached PDF).

Press the Tab key to move to the placeholder to change to English units at the placeholder. (e.g. type: t, =, tab key, desired units)

Once you complete that, lets find the matrix for X(t) in meters and feet, V(t) in feet per seconds, miles per hour and meters per second (just for practice).

Lets say we want to find the velocity of the ball at 8 seconds. Can we find this by either looking at the table or typing in V(8s) and then hitting the equal sign. MathCAD will automatically generate the number for us. Remember that if you change the units for the solution MathCAD provides, it will change the solution to match your units.

There are variety of things you can do with MathCAD and other engineering software. Play around with these tools available to you and use it to your advantage. Remember that software are designed for you and not the other way around. For you to have something to look at, I uploaded a PDF of the tutorial along with a MathCAD file.

Download PDF

http://www.sazzadhossain.org/wp-content/uploads/2011/02/Mathcad_UniformAcceleration.pdf

Download MathCAD File

http://www.sazzadhossain.org/wp-content/uploads/2011/02/Mathcad_UniformAcceleration.zip

Last Updated: April 03, 2011