**Chapter 2**

**1-d Motion: Kinematics**

**Introduction lecture**

**Main topics:**

Kinematic, defined

Variables

Displacement vs. distance

Speed vs. Velocity

Acceleration

Instantaneous variables

Free fall

Graphical analysis

Kinematic, defined

Variables

Displacement vs. distance

Speed vs. Velocity

Acceleration

Instantaneous variables

Free fall

Graphical analysis

**Kinematics**

The study of motion due to forces and energy is called Mechanics.

We divide this into two areas

Why things move.

How things move.

Kinematics is study of how things move.

Big picture: it relates position, velocity, acceleration, and time.

Variables

time: t

position: x

velocity: v

acceleration: a

If something is not constant, meaning allowed to change, then you can write, 'the change in x' as

This is read as: 'The change in position equals the final position minus the initial position.

This is true for time, velocity and acceleration as well.

Building blocks

Particle model: one of the principles of motions states that all motion of an object will be about its center of mass. This leads to a nice simplification. We can view objects as if they were just a 'dot' a particle with total mass. It isn't the ultimate model but it will suffice for a good while yet.

Reference frame: kinematics and dynamics are matters of a 'point of view'. To one person something might be moving away, while to another towards. A reference frame is ones standard to compare measurements. They will consist of locations and times, and can be different from others reference frames.

Location

Distance vs Displacement

Displacement: change in position.

Distance is 'how far' something has traveled

velocity vs. speed

AVERAGE

speed: distance divide by time

velocity: change in position (displacement) divided by time

Note: if we loose the "average" then you can think of speed as a velocity with no direction

Second Note: we don't use 'average' very often.

Acceleration

If an objects speeds up or slows down it accelerates.

Velocity is not acceleration, and acceleration is not velocity.

Acceleration is defined as the change of velocity. Here is an average acceleration.

note: deceleration is not a nice word.

If an object 'speeds up' then its acceleration is in the same direction as its velocity.

If it 'slows down' then its acceleration is opposite its velocity.

Instantaneous

Average velocity, average speed, acceleration, position. These variables all change.

Often.

Continuously.

We measure things only as fast as we are able, taking small 'steps' between measurement. Giving us an array of positions, velocities, and times.

Yet our world is a fluid place, we don't 'jump' from one location to the next, but rather move smoothly to it.

Thus at any given instant we will have only one, position, velocity, or time, etc.

Mathematically to solve for instantaneous variables we use limits.

Constant Acceleration

Although not always true, much motion is nature is made up of constant acceleration.

Nicely the average value and the instantaneous value of acceleration are the same.

You'll note that our variables are linked to each other: position, velocity, acceleration, and time.

Constant acceleration means that your velocity is changing at a constant rate.

For example you could be going 2 m/s then 4 m/s then 6 m/s and 8 m/s..... all in the same amount of time change.

We have defined kinematics as the study of how things move. How fast, How far, How long?

There are equations that describe this motion, three main ones.

Equations of motion

The top is a position equation.

Velocity equation.

Velocity without time (solved by substituting the first two)

Free fall

Free fall motion is defined as constant acceleration due only to gravity.

All objects will fall with the same acceleration, in the absence of air resistance.

The sign in important to note. We can choose up or down to be positive or negative, the trick is being consistent.

On a position graph

On a velocity graph

On a velocity graph