SCI340 L03_dva Position, velocity, and acceleration 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? The tortoise. The hare. They had the same speed. What do you mean by faster?

Velocity Rate of changing position average velocity = Dx Dt over entire interval

Poll Question Who had the fastest average speed? The tortoise. The hare. Their average speeds were the same. Over what time interval?

Speed Units distance = m/s time

Velocity as Slope D distance Velocity = = slope of graph! D time

Instantaneous velocity lim Dt0 finite Dt smaller Dt Young and Freedman, Figure 2.7

Velocity Dx Dt at one instant instantaneous velocity = lim

CPS Question Who had the fastest maximum instantaneous speed? The tortoise. The hare. Their instantaneous speeds were the same.

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

Speeds and Areas speed area = vDt = D(distance) time hare tortoise t0

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 Dv average acceleration = Dt over the entire interval Dv Dt at one instant instantaneous acceleration = lim

Poll Question What is the SI unit for acceleration? m. s. m·s. m/s.

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): position time

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

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