Kinematics - One Dimensional Motion
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How can we describe motion?

Let's forget about
what causes the actual motion

for right now and concentrate
on the actual motion

Displacement-Time-Velocity Diagram
Displacement-Time-Velocity Graphs
Displacement,, Velocity and Acceleration

A Position-Time Graph
of a car in
one-dimensional motion.

The graph illustrates where the car is at any given time.

The velocity and acceleration of the car can be determined from the slope of the graph.

Using your mouse pointer go ahead and change some of the position points!

The displacement of a particle is defined as its
change in position
in some time interval.

Displacement is a vector. A vector represents both a magnitude and a direction.

Distance is the length of a path followed by a particle. This is a scalar value.

The average speed of a particle is defined as the particle's
total distance
divided by the total time interval.

On the diagram, the average velocity is the slope of the line connecting the two points of interest.

What if, instead of the average velocity between TWO points,
I want to know the velocity at any ONE point?

We will need to find the object's Instantaneous Velocity.

Finding the tangent to a curve

Mechanical Universe

The velocity at any point is
the derivative of x wrt t
Mechanical Universe

How did Newton find the instantaneous velocity?

Acceleration occurs when the velocity of an object changes with time

The average acceleration of the particle is defined as the change in the velocity
divided by the time

The Instantaneous acceleration is the
limit of the average acceleration
as the change in time approaches zero.

A velocity-time graph

acceleration is the change in the velocity which is the change in the position wrt time.
acceleration is the derivative of the velocity wrt time and is the second derivative of the position wrt time

Java Motion Diagrams I,II,III

My Animated Gif explaining motion graphs.

Looking at the vectors involved

The Motion Equations

These motion equations are valid if the acceleration is constant. Currently we are only discussing the motion along the x-axis (1-D motion).

Mechanical Universe - The Law of Falling Bodies

Problem Solving