Assigned Groups
• Find which group you’re in
• Find where it is
• Sit there
• Be friendly
screen screen
1 2 3
4 5 6
7 8
Announcements
• Show your name tags!
• Please give Moodle your registered name
• Labs and discussions have already started
Objectives
• Relate distance, velocity, and acceleration.
• Interpret distance-time, velocity-time, and acceleration-time plots.
Standard
• Relate distance, velocity, and acceleration mathematically, graphically, and conceptually.
Describing Motion
It’s all math today
The Tortoise and the Hare
Told in words, formulas, and graphs
Question
Who was faster?
A. The tortoise.
B. The hare.
C. They had the same speed.
D. What do you mean by faster?
Group Work: Graph
Describe the Tortoise-and-hare race using a position-time graph.
• Same axes• One world-line for tortoise, another for hare• Indicate significant times and positions
Speed
average speed = dt
over entire interval
instantaneous speed = lim dt
at one instantt 0
Rate of changing position
Speed as Slope
Speed = distance
time
distance
time
= slope of graph!
d
t
Question
Who had the highest average speed?
A. The tortoise.
B. The hare.
C. Their average speeds were the same.
D. Over what time interval?
Poll Question
Who had the highest instantaneous speed?
A. The tortoise.
B. The hare.
C. Their instantaneous speeds were the same.
D. At what time?
Speed Units
distance
time= m/s
Group Work: Graph
Describe the Tortoise-and-hare race using a velocity-time graph.
Distance Change as Area
• What are the areas under the tortoise’s and hare’s velocity-time plots?
spee
d
timet1 t2 t3
hare
tortoise
area = vt = distance)
t0 t4
Group Work: Graph
A car waits at a stop light for 5 seconds, smoothly accelerates to 15 m/s over 5 seconds, and then continues at 15 m/s. Describe the car’s motion using a velocity-time graph.
Acceleration
Rate of changing velocity
average acceleration = vt
over the entire interval
instantaneous acceleration = lim vtt 0
at one instant
Acceleration Units
velocity
time=
s
m/s= m/s2
Group Work: Graph
What is the car’s acceleration at the different times? Describe the car’s motion using an acceleration-time graph.
Group Work: Compute
How far does the car travel:a. Between 0 s and 5 s?
b. Between 10 s and 15 s?
AccelerationStarting from a traffic light that turns green
d
t
v
t
a
t
area = velocity
area = distance
slope = velocity
slope = acceleration
Group Work 7
Describe four ways (x-t, v-t, a-t, words):
timeposi
tion
0
Group Work 7
Describe four ways (x-t, v-t, a-t, words):
timevelo
city
0
Group Work 7
Describe four ways (x-t, v-t, a-t, words):
time
acce
lera
tion
0
Group Work 7
Describe four ways (x-t, v-t, a-t, words):
A coconut hangs motionless from its tree, then drops with increasing downward speed until it lands on the ground, quickly coming to rest.
Formulas for Constant Acceleration
• Velocity change v = a t
• Velocity vt = v0 + v = v0 + a t
• Position change x = v0 t + 1/2 a (t)2
• Position xt = x0 + v0 t + 1/2 a (t)2
Reading for Next Time
• Vectors: how we handle quantities with directions
• Important vectors: position, velocity, acceleration, force
Top Related