Department

PhysicsCourse Code

PHYS 1110Professor

prof.stevenpollockLecture

1 1D - 1

9/28/2013 Dubson Notes University of Colorado at Boulder

Motion in one dimension (1D)

In this chapter, we study speed, velocity, and acceleration for motion in one-dimension. One

dimensional motion is motion along a straight line, like the motion of a glider on an airtrack.

speed and velocity

distance traveled d

speed , s = , units are m/s or mph or km/hr or...

time elapsed t

speed s and distance d are both always positive quantities, by definition.

velocity = speed + direction of motion

Things that have both a magnitude and a direction are called vectors. More on vectors in Ch.3.

For 1D motion (motion along a straight line, like on an air track), we can represent the direction

of motion with a +/– sign

Objects A and B have the same speed s = |v| = +10 m/s, but they have different velocities.

If the velocity of an object varies over time, then we must distinguish between the average

velocity during a time interval and the instantaneous velocity at a particular time.

Definition:

change in position x

average velocity = v change in time t

f i 2 1

f i 2 1

x x x x x

vt t t t t

x = xfinal – xinitial = displacement (can be + or – )

+ = going right

– = going left

always!

B

vB = +10 m/s

vA = –10 m/s

A

x

0

(final)

(initial)

x

0

x1

x2

1D - 2

9/28/2013 Dubson Notes University of Colorado at Boulder

Notice that (delta) always means "final minus initial".

x

vt

is the slope of a graph of x vs. t

Review: Slope of a line

Suppose we travel along the x-axis, in the positive direction, at constant velocity v:

x

0

start

x

x

t

x2

t

x1

t1

t2

y

x

slope =

rise

run

=

=

x

t

= v

y-axis is x, x-axis is t .

x

y

y

x

y

x

slope =

rise

run

=

x

y

(+) slope

x

y

(–) slope

x

y

0 slope

y2 – y1

=

x2 – x1

(x1, y1)

(x2, y2)

1D - 3

9/28/2013 Dubson Notes University of Colorado at Boulder

Now, let us travel in the negative direction, to the left, at constant velocity.

Note that v = constant slope of x vs. t = constant graph of x vs. t is a straight line

But what if v constant? If an object starts out going fast, but then slows down and stops...

The slope at a point on the x vs. t curve is the instantaneous velocity at that point.

Definition: instantaneous velocity = velocity averaged over a very, very short (infinitesimal)

time interval

t0

x d x

v lim t d t

= slope of tangent line. In Calculus class, we would say that the

velocity is the derivative of the position with respect to time. The derivative of a function x(t) is

defined as the slope of the tangent line:

t0

d x x

lim

d t t

.

x

x

t

t

x

t

x

0

start

x

x < 0

t

t

slope = v =

x

t

< 0

x

slower

slope > 0 (fast)

t

slope = 0 (stopped)

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###### Document Summary

In this chapter, we study speed, velocity, and acceleration for motion in one-dimension. Things that have both a magnitude and a direction are called vectors. For 1d motion (motion along a straight line, like on an air track), we can represent the direction of motion with a +/ sign. = going left always! va = 10 m/s vb = +10 m/s. Objects a and b have the same speed s = |v| = +10 m/s, but they have different velocities. If the velocity of an object varies over time, then we must distinguish between the average velocity during a time interval and the instantaneous velocity at a particular time. X = xfinal xinitial = displacement (can be + or ) University of colorado at boulder distance traveleddspeed, s=,units are m/s or mph or km/hr ortime elapsedt change in positionxaverage velocity = v change in timet fi21fi21xxxxxvttttt .

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