1.5:  Constant acceleration and the equations that go with it.

Put your math hat on and fasten your seat belt.  We're about to do a pile of algebra with our equations of motion.

Key concept: 

Constant acceleration.  In a lot of situations, the acceleration of an object is a constant value... or it's close enough for us to make the assumption that it is constant.

Textbook Section:  2-5

Even though it looks like things are getting difficult, assuming constant acceleration actually makes the math easier.  If acceleration is not constant, we must use calculus for our equations of motion.

A variable switch before we begin:  We have been using the variables xi and xf for initial and final position.  We will still use the same concept, but now x (no subscript) will be the final value, and x0 (pronounced 'x naught') will be the initial value.  We will make the same switch with the velocity variables.

Ready?  Here we go:

• If acceleration is a constant: 

Verify for yourself that this is the same equation we saw in section 1.4, but with the changes discussed above

• Do the algebra to solve this equation for v:

Make sure you can do the same algebra that I just did.

Does that equation look familiar?  Like, maybe, y=mx+b?  If you have a graph of velocity vs. time, constant acceleration means that the graph will be a straight line.  Remember what I said about making things easier?  Straight line graphs are easy.

If the graph of velocity vs. time is a straight line, acceleration is constant.

Another variable switch:  To save some space while writing these things out, we will omit the delta symbol.

if the initial time t0 = 0, we can write

Just understand that "t" refers to a time interval, not an absolute time measurement.

If acceleration is constant, we know two things:

and

That second one is only true if the graph is linear.  You can't just add final and initial and divide by two for any other shape of graph.  We can take the two equations above, and bring in a third equation from earlier in the chapter:

And with just a little bit of algebra... or maybe quite a lot of algebra, we get the following four equations: