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.

Tortoise and hare race start distance time finish hare tortoise t1t1 t3t3 hare restshare finishes t2t2 tortoise finishes

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 = xx tt 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 d  t t

Instantaneous speed finite  t Young and Freedman, Figure 2.7 smaller  t lim t0t0

Speed xx tt at one instantinstantaneous speed = lim tt 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 plotmotion 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 = v  t x f = x i +  x = x i + v  t Can also use this with average v

Speeds and Areas speed time t1t1 t2t2 t3t3 hare tortoise area= v  t =   distance) t0t0 t4t4