Assigned Groups

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4 5 6

7 8

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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