Motion in One Dimension

Motion in One Dimension

Displacement and Velocity

Motion

1. One Dimensional motion is the simplest form of motion

A.

An example of one dimensional motion is the motion of a commuter train on a straight track

B.

The train can move either forward or backward along the tracks

C.

It cannot move left or right, or up and down

2. Motion takes place over time and depends upon the frame of reference

A.

The train can start at its station and can move to another station farther down the tracks

B.

The Earth is spinning on its axis , so the train, the stations, and the tracks are also moving around
the axis

C.

At the same time, Earth is moving around the sun

D.

To help determine the motion taking place, choose a frame of reference against which you can
measure changes in position

E.

When you select a frame of reference, it remains fixed for the problem in question and has an origin,
or starting point, from which the motion is measured

F.Any frame of reference can be chosen as long as it is used consistently

Displacement

A.

As an object moves from one position to another, the length of the straight line drawn from its initial

position to the object’s final position is called the displacement of the object

B.

Displacement is a change in position

1.

Consider an object moving relative to a ruler. We could think of the ruler being an x-axis. As an object

moves from left to right along the x-axis from an initial position, xi, to a final position, xf the displacement is the
difference between its final and initial positions or xf - xi.

2.

The Greek letter delta before the x denotes a change in the position of an object, or displacement

3.

Displacement = change in position = final position - initial position

Displacement (cont)

C.

Displacement is not always equal to the distance traveled

D.

Displacement can be positive or negative

1.

Displacement also includes a description of the direction of motion (a vector)

2.

In one dimensional motion, there are only 2 directions in which an object can move, and these

directions can be described as positive or negative

3.

Right or east, will be considered positive. Left or west will be considered negative

4.

Up or north, will be considered positive, and downward or south will be considered negative

Multiple Choice

Is displacement equal to distance?

• yes

• no

Velocity

A.

Where an object started and stopped does not completely describe the motion. Speed is also

important when evaluating motion

B.

Average velocity is displacement divided by the time interval

1.

Average velocity = change in position/change in time = displacement / time interval

2.

Average velocity is not always equal to the average of the initial and final velocities. Example:

consider a car trip to a friend’s house 370 km to the west along a straight highway. If you left your house
at 10 am and arrived at your friend’s house at 3 pm (5 hours) your average velocity would be

-370km/5.0 hours = -74 km/hour = 74 km/h west

3. You probably didn’t drive exactly 74 km/h at every moment. You could have driven less than that at
times, or more than that at times

Velocity is not the same as speed

A.

Velocity is not the same as speed

1

In everyday language, the terms speed and velocity are used

interchangeably.

2.

Speed has no direction, only magnitude

3.

Velocity has magnitude and direction

Velocity can be interpreted graphically

Graphically

1.

Velocity can be determined if an object’s position is known at specific times along its

path

2. Graph the motion

3. Time is plotted on the x-axis and position is plotted on the y-axis

4. For any position-time graph, we can determine the average velocity by drawing a
straight line between any 2 points

5. The slope of the line is the average velocity between the positions and times
represented by these points

6.

Slope = rise/run = change in position/change in time = xf - xi / tf - ti

Instantaneous velocity vs average velocity

A.

Consider a position vs time graph that is a curve

1.

To determine the velocity at some instant, we study a small time interval near

that instant

2.

Choose a point on the curve and draw a line that is tangent to that point on

the curve, determine the slope at that point and it will give you the instantaneous
velocity