Ch 2: Motion in One Dimension

In chapter 2 we will take a close look at motion in one dimension. The topic is called kinematics and looks at motion without needing to know about the forces that cause the motion (that will follow shortly!). The idea of VECTOR versus SCALAR is critically important as will be learning how to read word problems, set up problems properly, and interpret motion based on graphs and diagrams.

Establishing good habits at this point in the course will help you to succeed. EVERY concept is built upon the foundations laid in the weeks prior. If you miss something, it will have a strong ripple effect for the remainder of the course. This course truly requires active participation- PRACTICE of skills- accomplished through completing HW and solving problems in lab and in lecture class.

The Physics Classroom Link to 1D motion

Displacement

The change in position of an object from start to finish without regard to the path traveled to change its position. Imagine tying a string between the start and end positions and measuring its length and the angle or compass direction it went. Displacement is a VECTOR which means that it has a size (magnitude) and a direction of motion. Displacement is measured in meters.

Distance is different than . Distance is just how much ground the object covered during its displacement- like the odometer on your car that measures the miles traveled- and has no consideration of direction traveled. Distance is a SCALAR quantity- just a size- no direction.

Velocity

The vocabulary we use in physics is pretty specific and technical. Speed is often used interchangeably with velocity in common conversation, BUT they have very different meanings in physics. Speed is a SCALAR and velocity is a VECTOR. Velocity = displacement / time with the units of m/s

Average speed = total distance / total time
Sometimes the average speed value is useful, but it really doesn't say much about the nature of the motion. If you were stopped at a stop light, held up in slow traffic, and then exceeded the speed limit to make up time, the average speed might be the same value as someone who drove a constant speed throughout.

Instantaneous Velocity

At any moment in time one may determine the object's instantaneous velocity. On a graph of displacement vs. time, the instantaneous velocity is the slope of the line at that point. When a police radar gun senses your car's speed, they are actually reading the instantaneous velocity at the moment the beam hits and reflects back from your vehicle.
instant_vel
Inst_Vel_graph

Relative Velocity

The slope of the displacement vs. time graph will yield the velocity value. Comparing slopes allows you to easily compare relative velocities. The greater the slope, the greater the velocity. A negative slope means a velocity in the opposite direction.
relative-velocity.gif
fast_slow_dot_diagram
The dot diagrams also show relative velocity by the spacing of the dots. Dots represent equal amounts of time, typically one second.
Faster = bigger spaces between dots. Slower = closer spaced dots.

Acceleration

Acceleration is just the rate of change of velocity and is measured in m/s^2
Since velocity is a vector so is acceleration! The magnitude and direction BOTH matter...

Average Acceleration

The average acceleration is simply the final velocity minus the initial velocity all divided by time.

Instantaneous Acceleration

The slope of the velocity vs. time graph at any instant will yield the value of the instantaneous acceleration of the object.
instantaeous_accel_100.jpg

Companion Motion Graphs

Quite a bit of information is provided by companion graphs of motion. It is critically important that you learn the two sets of graphs below!

Constant Velocity

Constant Acceleration

Const Vel graphs.png
displacement vs. time .....velocity vs. time ......accel. vs. time
constantaccelerationcompaniongraphs.gif
....displacement vs. time ...velocity vs. time.......accel. vs. time
The CURVE of the d vs t graph is only found with acceleration

The Moving Man

Learn about position, velocity, and acceleration graphs.
Move the little man back and forth with the mouse and
plot his motion. Set the position, velocity, or acceleration
and let the simulation move the man for you.

PhET Java simulation
The Moving Man
Click to Run