Motion in a Straight Line Position Velocity Acceleration

Name Some Things That Move Vehicles – cars, planes, etc. Animals – birds fly…fish swim…people walk Molecules – vibrational, rotational and translational motion The Earth, the moon, the sun, the Galaxy…the universe …everything moves…maybe…

So…then, what is motion? Motion is common to everything in the universe. That is why it is the beginning of the study of physics. Motion is described by three criteria: position, velocity and acceleration.

POSITION Must be defined relative to a reference point. Must be defined using both magnitude and direction.

Displacement and Distance A objects displacement is defined as the separation between an object and a reference point. It must be defined by magnitude and direction.

… and Distance? Distance is simply the separation between any two points. It is defined simply by magnitude.

Scalars and Vectors

What is a Scalar? A scalar is a quantity that is described only by magnitude…such as distance. The distance from Gainesville to Bronson is 22 miles.

What Is a Vector? A vector is a quantity that must be described by magnitude and direction. The displacement between Gainesville and Bronson is 22 miles at 32 degrees south of west.

Speed and Velocity The relationship between motion and time.

Speed Speed is defined as the distance traveled per unit time. It is a scalar quantity. It units are meters per second (m/s).

Velocity Velocity is displacement per unit time. It is a vector quantity. Its units are meters per second (m/s).

More Velocity It is defined relative to a reference point. Velocity describes both speed and direction. Depending on your direction, it can be negative or positive.

Now Remember This Velocity is a vector quantity. Speed is a scalar quantity. Displacement is a vector quantity. Distance is a scalar quantity.

Definitions Average Velocity Instantaneous Velocity Relative Velocity

Acceleration Consider an airplane taking off. As it goes down the runway it increases its speed until it is going fast enough to “lift off” the ground.

Son of Acceleration The increase of velocity per unit time is called acceleration. It is the rate of change of velocity. Its units are meters per second squared (m/s^2).

Average Acceleration Average acceleration is the change in velocity divided by the change in time.

…and some notes… Acceleration is a vector. It can be positive or negative. At rest means initial time is zero. When velocity is constant, acceleration is zero. When velocity increases at a constant rate, acceleration is uniform.

The Motion Equations

Displacement & Acceleration By factoring out final velocity, we can get displacement in terms of initial velocity and uniform acceleration.

…and what if you don’t have time? Let’s factor time out of the equation and see what we get…

In Summation Now we have equations that will enable us to solve for time, velocity, displacement and acceleration for horizontal straight line motion.

…but wait a minute… What if it’s vertical straight line motion…say, like a rocket going up at Cape Canaveral?!?

It’s really quite simple When you are traveling in a vertical direction, acceleration is always the same. It is the acceleration of gravity, g, which always has the same value.

GRAVITY

Vertical Motion For vertical motion problems, simply substitute g for a in any of the straight-line motion equations.