Describing Motion

kinematics

§2.1–2.2

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?

Speed

average speed = xt

over entire interval

Rate of changing position

CPS 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

Example Problem

You are working for the summer on the Wyoming Search and Rescue Squad when you get a call of a downed aircraft. The plane took off from Cheyenne at 12:15, flew north 100 miles and then 80 miles in a direction 30° north of west, where it vanished from radar at 1:05.

What was the average speed of the plane?

Speed as Slope

Speed = distance

time

distance

time

= slope of graph!

d

t

Instantaneous speed

finite t

Young and Freedman, Figure 2.7

smaller t limt0

Speed

xt

at one instantinstantaneous speed = limt 0

= dx/dt

CPS Question

Who had the fastest maximum instantaneous speed?

A. The tortoise.

B. The hare.

C. Their instantaneous speeds were the same.

Illustrating Motion

Young and Freedman, Fig. 2.8

x-t plot motion diagram

Can we make a motion diagram of this race?

Group Work

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

Constant-Velocity Motion

• v = x/t = constant throughout process

• x = vt• xf = xi + x = xi + vt

• Can also use this with average v

Speeds and Areassp

eed

timet1 t2 t3

hare

tortoise

area = vt = distance)

t0 t4