Describing Motion

Position, velocity, and acceleration

§2.1–2.4

The Tortoise and the Hare

Told in words, formulas, and graphs

Group Work

Describe the Tortoise-and-hare race using a position-time graph.

CPS Question

Who was fastest?

A. The tortoise.

B. The hare.

C. They had the same speed.

D. What do you mean by faster?

Velocity

average velocity = xt

over entire interval

Rate of changing position

Poll Question

Who had the fastest average speed?

A. The tortoise.

B. The hare.

C. Their average speeds were the same.

D. Over what time interval?

Speed Units

distance

time= m/s

Velocity as Slope

Velocity = distance

time

distance

time

= slope of graph!

d

t

Instantaneous velocity

finite t

Young and Freedman, Figure 2.7

smaller t limt0

Velocity

xt

at one instantinstantaneous velocity = limt 0

CPS Question

Who had the fastest maximum instantaneous speed?

A. The tortoise.

B. The hare.

C. Their instantaneous speeds were the same.

Group Work

Describe the Tortoise-and-hare race using a velocity-time graph.

Speeds and Areassp

eed

timet1 t2 t3

hare

tortoise

area = vt = distance)

t0 t4

Group Work

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 speed-time graph.

Acceleration

Rate of changing velocity

average acceleration = vt

over the entire interval

vt

at one instant

instantaneous acceleration = limt 0

Poll Question

What is the SI unit for acceleration?

A. m.

B. s.

C. m·s.

D. m/s.

E. m2/s.

F. m/s2.

G. m2/s2.

Group Work

In the car scenario:

What is the car’s acceleration during the different segments of its motion?

Describe the car’s motion using an acceleration-time graph.

Group Work

Describe four ways (x-t, v-t, a-t, words):

timeposi

tion

0

Group Work

Describe four ways (x-t, v-t, a-t, words):

timevelo

city

0

Group Work

Describe four ways (x-t, v-t, a-t, words):

time

acce

lera

tion

0