+ Week 7 10 th grade science

+ Must Do Consider the following statement by a student “ Δ x/ Δ t gives the velocity for an interval. To find the velocity at an instant, divide the position a that instant by the time at that instant: v = x/t.” Does this statement express the same ideas as we discussed last week or does it express different ideas? Is v = x/t a precise mathematical statement of the definition of instantaneous velocity? Explain.

+ Sample problem Wheat is leaving from many countries. The wheat export reate for a country tells how fast wheat is leaving the country. An operational definition of wheat export rate is: Mass of wheat exported during a certain amount of time That amount of time This rate varies throughout the year and from year to year. Make a mathematical analogy between wheat export rate and velocity. Tell what corresponds to instantaneous velocity, displacement, and duration.

+ Sample Solution Wheat export rate corresponds to instantaneous velocity. Both are ratios. Both quantities are not necessarily constant. To compute both, we must consider a small enough interval that rate is nearly constant. To compute both, we must consider a small enough interval that the rate is nearly constant. (We cannot calculate the export rate of one year if we want information about the high and low rates during the year). The amount of wheat exported in an interval of time corresponds to displacement. (numerator) Duration of motion corresponds to duration of wheat exportation. (Duration is in the denominator)

+ Exit Ticket One observation commonly taken during a physical examination is the patient’s pulse rate before, during, and after vigorous exercise. How would you expect the pulse rate to vary in such an examination? Give an operational definition of pulse rate. Your definition should work when the time of measurement is of any short duration of time, not a special amount of time like one minute or 10 seconds. Make a mathematical analogy between pulse rate and velocity. Identify what corresponds to instantaneous velocity, displacement, and duration, and tell how corresponding quantities are alike.

+ Changing Velocity Create an event in your table of contents called “Changing velocity” and title the next blank right page the same. Work with your table partners to complete the handout. This is a class copy do not write on it. Copy any pertinent information/diagrams from the sheet to your notebook for your notes.

+ Practice Problems A car and a truck are at a gas station. At 2:00 the truck starts traveling along the highway at a constant speed of 54 mph. A quarter of an hour later, at 2:15, the car starts traveling along the same highway with a constant speed of 60 mph. At what time will the car catch up with the truck? Let Δ t be the number of hours the car travels between leaving the gas station and catching up with the truck. Write an expression for the car’s distance from the gas station Δ t hours after the car starts. Write an expression fpr the truck’s distance from the gas station Δ t hours after the car starts

+ Two cars start from the same place on the same road but at different times. Car 1 travels with constant velocity v 1 for a distance d, and then stops. Car 2 starts at time t after car 1, travels with constant velocity v 2 until it has gone the same distance d, and then stops. Write an interpretation of each of the following expressions, if such an interpretation exists. (Some expressions may have no interpretation relevant to the motion described.) d/v 2 v 1 t d/t v 2 t