## 3.2 - Speed

By definition,

As an example, a student lives 20 kilometers from Thayer. It takes her a half hour to get to school in the morning. Her average speed is the comparison between the distance covered and the time that it took. That is, 20 Km/0.5 hr = 40 Km/hr. Although any unit of distance divided by any unit of time would be a unit of speed, the accepted base unit of speed is meters/second (m/s). 40 Km/hr is an average speed of 11 m/s. Is that fast or slow? 40 Km/hr is 24 miles per hour

Just because her average speed was 11 m/s does that mean that she was traveling that speed the entire time? Of course not, she had to speed up onto the highway as well as slow down off the highway. 11 m/s is her average speed. To know how fast she was traveling at any instant in her trip, we need more information.

Realistically, you can never know her speed at any one instant of time. Speed can only be determined during a length of time. If we make that length of time small enough, it can be considered an instant. The speed calculated during a small length of time is called the

Mathematically:

__speed is the rate at which an object’s distance changes from a given location__. It is a comparison between the change of distance a moving object has to the time it took to move.As an example, a student lives 20 kilometers from Thayer. It takes her a half hour to get to school in the morning. Her average speed is the comparison between the distance covered and the time that it took. That is, 20 Km/0.5 hr = 40 Km/hr. Although any unit of distance divided by any unit of time would be a unit of speed, the accepted base unit of speed is meters/second (m/s). 40 Km/hr is an average speed of 11 m/s. Is that fast or slow? 40 Km/hr is 24 miles per hour

Just because her average speed was 11 m/s does that mean that she was traveling that speed the entire time? Of course not, she had to speed up onto the highway as well as slow down off the highway. 11 m/s is her average speed. To know how fast she was traveling at any instant in her trip, we need more information.

Realistically, you can never know her speed at any one instant of time. Speed can only be determined during a length of time. If we make that length of time small enough, it can be considered an instant. The speed calculated during a small length of time is called the

**instantaneous speed**.Mathematically:

Let's walk through some problem-solving techniques:

## 3.2 Sample Problems

## Click __HERE __for more motion problem-solving practice.

How Fast is Fast?

**Fastest Humans**

__Sprint:__Usain Bolt: (Jamaica) 100 meters in 9.58 seconds on 8/16/09. Ave. speed = 10.44 m/s (23.3 mi/hr)

Video of Bolt's record run:

__Marathon:__Patrick Makau (Kenya) 26.2 miles in 2:03:38 on 9/25/2011. Avg. speed = 5.68 m/s (12.8 mi/hr). Avg. pace = 4 minutes, 43 seconds per mile!

**Fastest Animals**

__Land__: Cheetah top speed 31.5 m/s (71.0 mi/hr)

__Air__: Peregrine Falcon diving top speed 90.3 m/s (202 mi/hr)

__Sea__: Sailfish top speed 30.5 m/s (68 mi/hr)

**Fastest Machines**

__Land Speed:__Thrust SSC (land car): ave. speed = 339 m/s (763 mi/hr)

__: Space Shuttle: ave. speed = 7,800 m/s (17,500 mi/hr)__

Air

Air

**QUESTIONS:**

1. If Usain Bolt could go his average speed for the 100 m dash, how long would it take him to run a marathon?

2. How many times faster is the space shuttle than a peregrine falcon?

3. How long would it take a Cheetah to do the 100 m dash?