physics 121: fundamentals of physics i

PHYS 121University of MarylandD. Roberts

Physics 121:Physics 121:Fundamentals of Fundamentals of

Physics IPhysics ISeptember 13,

2006


Interpreting Position vs. Time GraphsInterpreting Position vs. Time Graphs

• Steeper slopes correspond to faster speed– Flat implies standing still

• Negative slopes -> negative velocity (motion to the left)

• The slope is the ratio of intervals, x/t, not a ratio of coordinates (not x/t)

• Be sure to look at the scale on the x-axis (time) and y-axis (position)– Also, make sure you know where the origin is– Positive position means to right of origin– Negative position means to left of origin


Interpreting Velocity vs. Time GraphsInterpreting Velocity vs. Time Graphs

• Positive velocity means moving to the right• Negative velocity means moving to the left• Flat (constant) velocity just means velocity isn’t

changing (constant motion)– Does NOT mean it isn’t moving– Zero velocity means it isn’t moving

• BIG THING: pay close attention to the sign (positive or negative) of the velocity– Tells you direction

? Consider the following velocity vs. time graph. Write Consider the following velocity vs. time graph. Write down a description of the person’s motion with as down a description of the person’s motion with as much detail as possible.much detail as possible.At the end of the motion, the person’s displacement is:At the end of the motion, the person’s displacement is:

Posi

tive

Neg

ativ

e

Not e

nough in

form

atio

n

None

of the

abo

ve

25% 25%25%25%

1 2 3 4 5

Velocity vs. Time

-6

-4

-2

0

2

4

6

0 2 4 6 8

time (s)

v (

m/s

)

1. Positive2. Negative3. Not enough information4. None of the above


Average AccelerationAverage Acceleration

• We need to keep track not only of the fact that something is moving but how that motion is changing.

• Define the average acceleration by

a

av

t

change in velocity

time it took to make the change


Technical term alert!Technical term alert!

• Note that in physics we use the term “acceleration” in a technically defined way:– “acceleration” = changing velocity

• The object may be speeding up or slowing down or keeping the same speed and changing direction. We still say “it is accelerating.”

• In common speech “acceleration” = speeding up,“deceleration” = slowing down, and “turning”=changing direction.

• How many (physics) accelerators are there on your car?


Average AccelerationAverage Acceleration

Figure 2.9

Note!


Uniformly changing motionUniformly changing motion

• If an object moves so that it changes its velocity by the same amount in each unit of time, we say it is in uniformly accelerated motion.

• This means the average acceleration will be the same no matter what interval of time we choose.

av

ta

v a t

v t v t a t

v v a tfinal initial

0

0

2 1 0

0

( ) ( )

Velocity as a function of time

0

2

4

6

8

10

-5 0 5 10 15

t (sec)

v (m

/s)


Instantaneous accelerationInstantaneous acceleration

• Sometimes (often) an object will move so that sometimes it speeds up or slows down at different rates.

• We want to be able to describe this change in motion also.

• If we consider small enough time intervals, the change in velocity will look uniform — for a little while at least.

0limt

v dva

t dt


Relationship Between Acceleration and VelocityRelationship Between Acceleration and Velocity

• Uniform velocity (shown by red arrows maintaining the same size)

• Acceleration equals zero


Relationship Between Velocity and AccelerationRelationship Between Velocity and Acceleration

• Velocity and acceleration are in the same direction• Acceleration is uniform (blue arrows maintain the same length)• Velocity is increasing (red arrows are getting longer)• Positive velocity and positive acceleration


Relationship Between Velocity and AccelerationRelationship Between Velocity and Acceleration

• Acceleration and velocity are in opposite directions• Acceleration is uniform (blue arrows maintain the same length)• Velocity is decreasing (red arrows are getting shorter)• Velocity is positive and acceleration is negative

physics 121: fundamentals of physics i

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