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### Unit 2 CVM

Instantaneous velocity and graphical representations of positon vs. time

Objectives

- I can…
- Identify an object’s direction of motion, initial position, and relative speed from a position vs. time graph
- Solve for time, velocity, or distance in problems using the constant velocity equation
- Draw 2 graphical representations of an object’s position vs. time.

Instantaneous Velocity (or simply velocity)

- This refers to the specific velocity at specific time
- As opposed to an average velocity
- Units (m/s)

My apologies!symbol Corrections

Y = M X + B

x = v t + x0

Y = M X + B

x = v t + x0

If V is constant, than it is equivalent to V0, so the equation becomes:

Constant Velocity Equation

or

Quick Note:Speed

- Speed is velocity without a direction
- i.e. 30m/s as opposed to 30m/s north

- This makes speed a scalar and velocity a vector
- Speed is also the magnitude or absolute value of velocity

- What can you say about A’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

Position (m)

B

Time (s)

- What can you say about A’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

- What can you say about B’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

Position (m)

B

Time (s)

- What can you say about A’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

- What can you say about B’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

- Which one has a greater velocity?
- How do you know?

Position (m)

B

Time (s)

- What can you say about A’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

Position (m)

A

B

Time (s)

- What can you say about A’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

- What can you say about B’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

Position (m)

A

B

Time (s)

- What can you say about A’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

- What can you say about B’s
- Direction of motion? +/-?
- Initial Position? +/-/0?
- Velocity? +/-?

- Which one has a greater SPEED?
- How do you know?

Position (m)

A

B

Time (s)

Constant velocity problems

- Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in:
- 1.00 s?
- 2.00 s?

Constant velocity problems

- Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in:
- 1.00 s?
- 2.00 s?

- The distance between home and first is 26.82m (88ft). How long would it take him to reach first base?

Constant velocity problems

- Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in:
- 1.00 s?
- 2.00 s?

- The distance between home and first is 26.82m (88ft). How long would it take him to reach first base?
- The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in 2010. It was recorded going 173.3km/h.
- How fast was this in m/s?

Constant velocity problems

- Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in:
- 1.00 s?
- 2.00 s?

- The distance between home and first is 26.82m (88ft). How long would it take him to reach first base?
- The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in 2010. It was recorded going 173.3km/h.
- How fast was this in m/s?
- It is 18.39m from the pitcher’s mound to home plate. How long did it take Aroldis’ pitch to reach home plate?

Constant velocity problems

- Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in:
- 1.00 s?
- 2.00 s?

- The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in 2010. It was recorded going 173.3km/h.
- How fast was this in m/s?
- It is 18.39m from the pitcher’s mound to home plate. How long did it take Aroldis’ pitch to reach home plate?

- Aroldis’ windup takes 2.35s and Ichiro is trying to “steal home”. Can he make it? (it is the same distance from 3rd base to home as it is from home base to 3rd)

Constant velocity problems

- Ichiro Suzuki, of the NY Yankees, hits a line drive and begins sprinting to first base. If he can run at 9.03m/s, how far does he get in:
- 1.00 s?
- 2.00 s?

- The fastest recorded pitch was thrown by Aroldis Chapman, of the Cincinnati Reds, in 2010. It was recorded going 173.3km/h.
- How fast was this in m/s?
- It is 18.39m from the pitcher’s mound to home plate. How long did it take Aroldis’ pitch to reach home plate?

- Aroldis’ windup takes 2.35s and Ichiro is trying to “steal home”. Can he make it? (it is the same distance from 3rd base to home as it is from home base to 3rd)
- If Ichiro “cheats out” by 2.50m, can he make it?

Graphical Representations of Position vs. TimeMotion Graphs

- A motion map represents the position, velocity, and acceleration of an object at various clock readings. (At this stage of the class, we will be representing position and velocity only.)
- Suppose that you took a stroboscopic picture of a car moving to the right at constant velocity where each image revealed the position of the car at one-second intervals.

- This is the motion map that represents the car. We model the position of the object with a small point. At each position, the object's velocity is represented by a vector.

- If the car were traveling at greater velocity, the strobe photo might look like this:
- Note the differences between the car traveling faster and the one traveling slower

- If the car were moving to the left at constant velocity, the photo and motion map might look like this:

- More complicated motion can be represented as well. photo and motion map might look like this:
- How would you describe the motion of the object here?

- More complicated motion can be represented as well. photo and motion map might look like this:
- How would you describe the motion of the object here?
- Here, an object moves to the right at constant velocity, stops and remains in place for two seconds, then moves to the left at a slower constant velocity.

Homework photo and motion map might look like this:

- Due 8/25
- Read and comment on 2 of your classmate’s blogs
- Please make the comments meaningful!

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