##

**Acceleration**

**We are often interested in how fast the velocity is changing. **"How
fast is something getting faster?" This is the **acceleration**.

**Acceleration is a change of velocity divided by a change of
time so it has units of (meters/second)/second. We will write this as
m/s/s or m/s**^{2} (there are **no** "square
seconds")**. As with the velocity, we can describe the average
acceleration or we can describe the instantaneous acceleration, the
acceleration right now, at this particular moment,**

**This, too, is a derivative,**

**As with the velocity, we will usually mean the instantaneous
acceleration if we simply say "the acceleration". We will often
restrict ourselves situations with a constant acceleration; in that
case the average acceleration is the same as the instantaneous
acceleration.**

**
**

**
**

**
We can take the definition of acceleration, turn it around, and
write**
**The distance an accelerating object moves is**

**Sometimes we may want to know about velocity and displacement and not
be interested in the time. For those situations,
we can play with these equations and come up with a third one --**

**v**^{2} = v_{i}^{2}
+ 2 a (x - x_{i})

With this equation, we might answer questions like, "Starting from rest
and accelerating at 1.5 m/s^{2}, **how far** has a car
traveled when its speed is 100 km/hr?"

**These are our Big Three Kinematics
Equations that we will use many, many times. Become familiar and comfortable
with them.**

**
**

**Consider a car that starts at rest and accelerates at 2 m/s/s
for 3 seconds.**

**At that time, t = 3 s, how fast is it going? and how far has it
gone?**

(c) 2005, Doug Davis; all rights reserved