IM: 7.5.8: Position, Speed, and Direction (Lesson)

Last updated 11 months ago

11 questions

8.1: Distance, Rate, Time

An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?

A train moves at constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute?

8.2: Going Left, Going Right

8.3: Velocity

IM: 7.5.8: Position, Speed, and Direction (Lesson)

Last updated 11 months ago

11 questions

8.1: Distance, Rate, Time

An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?

A train moves at constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute?

A car moves at a constant speed of 50 miles per hour. How long does it take the car to go 200 miles?

8.2: Going Left, Going Right

Complete the table and answer the follow-up questions. 

After each move, record your location in the table. Then write an expression to represent the ending position that uses the starting position, the speed, and the time. The first row is done for you.

How can you see the direction of movement in the expression?

Using a starting position p, a speed s, and a time t, write two expressions for an ending position. One expression should show the result of moving right, and one expression should show the result of moving left.

8.3: Velocity

A traffic safety engineer was studying travel patterns along a highway. She set up a camera and recorded the speed and direction of cars and trucks that passed by the camera. Positions to the east of the camera are positive, and to the west are negative.

Vehicles that are traveling towards the east have a positive velocity, and vehicles that are traveling towards the west have a negative velocity.

Complete the table with the position of each vehicle if the vehicle is traveling at a constant speed for the indicated time period. Then write an equation.

If a car is traveling east when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply two positive numbers, is the result positive or negative?

If a car is traveling west when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply a negative and a positive number, is the result positive or negative?

In many contexts we can interpret negative rates as "rates in the opposite direction." For example, a car that is traveling -35 miles per hour is traveling in the opposite direction of a car that is traveling 40 miles per hour.

IM: 7.5.8: Position, Speed, and Direction (Lesson)

An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?

A train moves at constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute?

IM: 7.5.8: Position, Speed, and Direction (Lesson)

An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?

A train moves at constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute?

A car moves at a constant speed of 50 miles per hour. How long does it take the car to go 200 miles?

After each move, record your location in the table. Then write an expression to represent the ending position that uses the starting position, the speed, and the time. The first row is done for you.

How can you see the direction of movement in the expression?

Using a starting position p, a speed s, and a time t, write two expressions for an ending position. One expression should show the result of moving right, and one expression should show the result of moving left.

Complete the table with the position of each vehicle if the vehicle is traveling at a constant speed for the indicated time period. Then write an equation.

If a car is traveling east when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply two positive numbers, is the result positive or negative?

If a car is traveling west when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply a negative and a positive number, is the result positive or negative?

What could it mean if we say that water is flowing at a rate of -5 gallons per minute?

Make up another situation with a negative rate, and explain what it could mean.

A car moves at a constant speed of 50 miles per hour. How long does it take the car to go 200 miles?

After each move, record your location in the table. Then write an expression to represent the ending position that uses the starting position, the speed, and the time. The first row is done for you.

How can you see the direction of movement in the expression?

Using a starting position p, a speed s, and a time t, write two expressions for an ending position. One expression should show the result of moving right, and one expression should show the result of moving left.

Complete the table with the position of each vehicle if the vehicle is traveling at a constant speed for the indicated time period. Then write an equation.

If a car is traveling east when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply two positive numbers, is the result positive or negative?

If a car is traveling west when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply a negative and a positive number, is the result positive or negative?

What could it mean if we say that water is flowing at a rate of -5 gallons per minute?

Make up another situation with a negative rate, and explain what it could mean.