Constant Rate of Change in Distance

The video tutorial explains how two quantities can vary together at a constant rate of change, using the example of a car traveling at a constant speed. It describes how changes in one quantity are proportional to changes in another, and illustrates this with a scenario where a car passes a mile marker at a constant speed. The tutorial analyzes changes in distance over various time intervals, demonstrating that the ratio of change in distance to change in time remains constant. It concludes with a calculation of distance traveled over a specific time interval.

What does it mean for two quantities to vary together at a constant rate?

• They change independently of each other.

• Changes in one are inversely proportional to changes in the other.

• Changes in one are directly proportional to changes in the other.

• They remain constant over time.

If x and y vary together at a constant rate of 3, what happens when x changes by 2?

• y does not change

• y changes by 1

• y changes by 3

• y changes by 6

What is a common example of a constant rate of change?

• Decreasing speed

• Fluctuating speed

• Constant speed

• Variable speed

In the car travel scenario, what does the variable 't' represent?

• The number of hours since passing a mile marker

• The distance to the next mile marker

• The speed of the car

• The number of miles traveled

How do T and D vary together in the car travel scenario?

• They do not vary

• They vary together at a constant rate

• They vary independently

• They vary inversely

What is the change in distance when T increases from 1 to 4?

• 192 miles

• 144 miles

• 96 miles

• 48 miles

What is the ratio of change in distance to change in time over the interval from T=1 to T=4?

• 48

• 24

• 60

• 36

What does a constant speed of 48 miles per hour imply about the ratio of change in distance to change in time?

• The ratio is always 24

• The ratio is always 48

• The ratio varies

• The ratio is always 96

How far does the car travel during the time interval from T=1.537 to T=2.859?

• 96 miles

• 120 miles

• 63.456 miles

• 48 miles

What is the change in time for the interval from T=1.537 to T=2.859?

• 2.322

• 1.859

• 1.5

• 1.322