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Average Velocity

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Average Velocity
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Students will learn the meaning of speed, velocity and average velocity.

Key Equations

Speed = distance/time

Average Velocity

$v_{avg} & = \frac{\boldsymbol{\Delta} x}{\Delta t} \\$

Guidance
Speed is the distance traveled divided by the time it took to travel that distance. Velocity is the instantaneous speed and direction. Average velocity is the displacement divided by the time.

Example 1

Pacific loggerhead sea turtles migrate over 7,500 miles (12,000 km) between nesting beaches in Japan and feeding grounds off the coast of Mexico. If the average speed of a loggerhead is about 45 km/day, how long does it take for it to complete the distance of a one-way migration?

Question: $t = ?$ [days]

Given: $d = 12,000 \ km$

${\;} \qquad v_{avg} = 45 \ km/day$

Equation: $v_{avg} = \frac{d}{t}$ therefore $t = \frac{d}{v_{avg}}$

Plug n’ Chug: $t = \frac{d}{v_{avg}} = \frac{12,000 \ km}{45 \ km/day} = 267 \ days$

Answer: $\boxed{\mathbf{267 \ days}}$

Time for Practice

1. Two cars are heading right towards each other, but are 12 km apart. One car is going 70 km/hr and the other is going 50 km/hr. How much time do they have before they collide head on?
2. You drive the 10 miles to work at an average speed of 40 mph. On the way home you hit severe traffic and drive at an average speed of 10 mph. What is your average speed for the trip?
3. The following data represent the first 30 seconds of actor Crispin Glover’s drive to work.
4. Time (s) Position (m) Distance (m)
0 0 0
5 10 10
10 30 30
15 30 30
20 20 40
25 50 70
30 80 120
1. Sketch the graphs of position vs. time and distance vs. time. Label your $x$ and $y$ axes appropriately.
2. Why is there a discrepancy between the distance covered and the change in position during the time period between $t = 25 \;\mathrm{s}$ and $t = 30 \;\mathrm{s}$ ?
3. What do you think is going on between $t = 10 \;\mathrm{s}$ and $t = 15 \;\mathrm{s}$ ?
4. What is the displacement between $t = 10 \;\mathrm{s}$ and $t = 25 \;\mathrm{s}$ ?
5. What is the distance covered between $t = 10 \;\mathrm{s}$ and $t = 25 \;\mathrm{s}$ ?
6. What is the average velocity during the first $30$ seconds of the trip?
7. What is the average velocity between the times $t = 20 \;\mathrm{s}$ and $t = 30 \;\mathrm{s}$ ?
8. During which time interval(s) was the velocity negative?
9. Sketch the velocity vs. time and speed vs. time graphs. Label your $x$ and $y$ axes appropriately.

1. 0.1 hours = 6 minutes

2. 16 mph

3. Discuss in class