 # Linear Motion

Using the applet in the previous section, you have created an equation for velocity as a function of acceleration and time. That equation assumed that the initial velocity was zero; to solve the problems which we are about to undertake, you will need the more general equation formed by adding the initial velocity to the right hand side.

Our ultimate goal is to determine the extent of your injuries following your fall from the roof. The first step is to understand the fall itself: how long did it take you to fall, and what was your velocity just before you hit the ground. In the applet below, you will be given the height from which you fell. From our previous discussion, you know the initial velocity and the acceleration. Your final position is at y = 0 (the ground), so you should be able to solve the following system of two equations:

position as a function of the initial position, initial velocity, acceleration and time

velocity as a function of the initial velocity, acceleration and time

for the final velocity and the time it took to reach the ground. Notice that because your position is decreasing (from your initial height to zero), your final velocity will be negative.

From an algebraic point of view nothing has changed:

in analyzing your fall, you were given the initial and final positions, the initial velocity and the acceleration;

in analyzing your stop, you are given the initial position (y = 0), the time it takes you to stop (which will be given to you by the applet) and the initial and final velocities.

So in each case you have a system of two equations in six variables (initial conditions count as variables for algebraic purposes):
initial position, final position, initial velocity, final velocity, acceleration and time.
And in each case, you are given the values of four of the variables. This means that you are left with a system of two equations with two unknowns, which of course has a unique solution.
Δy = 0 - yfinal
and yfinal is negative. All answers are entered in scientific notation (as x * 10y, where x >= 1 and x < 10), and the correct units must be supplied (m, s, m/s or m/s^2). Note that the applets use the symbol "^" to denote exponentiation.

You need a Java-capable browser to be able to use the applets. If they do not work with your Windows system, download the Java VM (Virtual Machine) for your version of Windows at the download section at java.sun.com.

The next section extends our work in this section to 2 dimensions.