A Review of Kinematics

Our study of Physics and rockets begins with some basic kinematics. Throughout this course, we will be applying principles that we learned in Physics to determine the flight profile and behavior of our rockets. I hope that we have already learned that there are many ways to solve different types of Physics problems. This class is going to try and put a lot of what you learned (but may not remember) together into one coherent process. In order to
do that, we need to do some review of the very first weeks of our Physics classes. Let's start with some definitions:

Distance - A scalar quantity (magnitude only) that represents the total path (or length) that an object moves. We'll measure distance in meters. 

Displacement (DX)- A vector quantity (has magnitude and a direction associated with it) that measures the straight line distance and direction from an objects initial position (Xo) to its final position (X). Mathematically, we say

 

DX = X - Xo

 

Here is a quick example:

 

A person walks 3 miles north and then walks 4 miles east. The total distance walked was 7 miles. But the displacement from the origin was 5 miles to the (roughly) northeast. (We will use trig in another lesson to determine the actual direction traveled.

Speed - A scalar quantity that indicates how fast something is moving. Speed is defined as the distance traveled per unit time. For example, your speedometer on your car measures your instantaneous speed (how fast you are going at a given instant) in miles per hour hour kilometers per hour.

Velocity

Velocity (v) is a vector quantity and is defined as the displacement per unit time. It is important to note that velocity has both a magnitude and a direction: 20 m/s down, 50 mph east, etc. We define velocity as:

where xf is our final position, xo is our initial position, tf is our ending time, and to is our starting time.

Velocity may also be stated in terms of instantaneous velocity (v) and average velocity (vave). Instantaneous
velocity is our velocity at any instant. Average velocity is the displacement per unit time, and depends solely on initial and final position. Average velocity may be found using the formula:

or by using the formula:

where vf is the final velocity and vo is the initial velocity. Note that this is just a straight mathematical average.

Acceleration

Average acceleration is a change in velocity per unit time, or

Acceleration is a vector quantity - it has both magnitude and direction. We can accelerate an object by changing its speed over a time interval, such as speeding up or slowing down in your car. We are familiar with the right hand gas pedal on a car - we call it the "accelerator." But the brake pedal can slow us down so it can also be called an "accelerator". We can also change the velocity of an object by changing the direction the object is moving. So in a car, the steering wheel is also a type of "accelerator". The units of acceleration are units of velocity per unit time. For example, (meters per second) per second, or m/s/s. We commonly write this as m/s2. For example, if a car accelerates from rest to 20 m/s in 5 seconds, then its acceleration is given by

Now that we have reviewed the basic definitions, We’ll do some problem solving in class. There are four basic equations that we will use in conjunction with the definitions above to determine the details of an object's motion in one dimension. These formulas are given to the right. We'll use the basic problem solving protocols discussed in Physics to work through our problems in class. 

For further review of the topics discussed, take a look at the following:

Distance and Displacement

Speed and Velocity

Acceleration

Gravity and Free Fall