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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 = dd tt over entire intervalinstantaneous speed = lim dd tt at one instant t0 Rate of changing position

Speed as Slope Speed =  distance  time distance time = slope of graph!  d d  t 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? speed time t1t1 t2t2 t3t3 hare tortoise area= v  t =   distance) t0t0 t4t4

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 = vv tt over the entire interval instantaneous acceleration = lim vv tt t0 at one instant

Acceleration Units velocity time = s m/s = m/s 2

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?

Acceleration Starting 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) : time position 0

Group Work 7 Describe four ways (x-t, v-t, a-t, words) : time velocity 0

Group Work 7 Describe four ways (x-t, v-t, a-t, words) : time acceleration 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 speeduntil it lands on the ground, quickly comingto rest.

Formulas for Constant Acceleration Velocity change  v = a  t Velocity v t = v 0 +  v = v 0 + a  t Position change  x = v 0  t + 1/2 a (  t) 2 Position x t = x 0 + v 0  t + 1/2 a (  t) 2

Reading for Next Time Vectors: how we handle quantities with directions Important vectors: position, velocity, acceleration, force