Exploring Direct Variation in Algebra II

The video tutorial explains how the distance an object travels in space varies directly with time, assuming no acceleration or net force. It introduces the concept of direct variation and constants of proportionality, using an example of an asteroid traveling 3000 miles in 6 hours to calculate the constant of variation. The tutorial demonstrates solving for the constant by dividing distance by time, resulting in a constant of 500 miles per hour.

In outer space, what does the distance an object travels depend on?

• The object's speed

• The amount of time it travels

• The object's mass

• The gravitational force

What assumption is made about the object traveling in outer space?

• It is affected by gravity

• It is not accelerating and there is no net force

• There is a net force acting on it

• It is accelerating

What does it mean for distance to vary directly with time?

• Distance is inversely proportional to time

• Distance is directly proportional to time

• Distance is equal to time squared

• Distance is independent of time

How can we express the relationship between distance and time using a constant of proportionality?

• Distance = Constant * Time

• Distance = Constant + Time

• Distance = Time / Constant

• Distance = Constant / Time

If an asteroid travels 3000 miles in 6 hours, what is the distance traveled?

• 1500 miles

• 6000 miles

• 3000 miles

• 500 miles

What is the equation used to find the constant of variation?

• Distance = Constant + Time

• Distance = Constant / Time

• Distance = Constant * Time

• Distance = Time / Constant

How do you solve for the constant of variation?

• Multiply distance by time

• Divide distance by time

• Add distance and time

• Subtract time from distance

What is the constant of variation if an asteroid travels 3000 miles in 6 hours?

• 300 miles per hour

• 600 miles per hour

• 500 miles per hour

• 1000 miles per hour

What is another term for the constant of variation?

• Constant of acceleration

• Constant of proportionality

• Constant of speed

• Constant of distance