0827

Quiz

1.  Give the definition of the rate of change of A with respect to B.

Some incorrect answers:

• A divided by B
• the proportion of A to B
• A / B
• rate of change of A / rate of change of B

Correct answer: 

• rate of change of A with respect to B is change in A / change in B

2.  Give the definition of velocity.

Velocity is the rate at which position changes with respect to clock time.

This is expressed as

• average velocity = change in position / change in clock time.

3.  If I drive from milepost 274 to milepost 130 between 12:30 p.m. and 2:40 p.m. on the same day then what is my average velocity?

• average velocity

= change in position / change in clock time

= (130 miles - 274 miles) / (2:40 p.m. - 12:30 p.m.)

= -144 miles / (2 hr 10 min)

= -144 miles / (130 minutes)

= -1.107 miles / minute.

4.  Give the definition of acceleration.

Acceleration is rate of change of velocity with respect to clock time, which is change in velocity / change in clock time.

5.  If my speedometer reads 10 mph at clock time t = 5 seconds and 70 mph at clock time t = 25 seconds, then if velocity is always in the positive direction what is my average acceleration?

• average acceleration

= change in velocity / change in clock time

= (70 mph - 10 mph) / (25 sec - 5 sec)

= 60 mph / (20 sec)

= 3 mph / sec.

6.  Sketch a possible graph of position vs. clock time for the situation of #3. 

• What property of the graph represents the change in position and what property represents the change in clock time?

The change in clock time is represented by the run of the graph between two points, and the change in position by the rise.

• What property of the graph represents the average velocity between the two given points?

The slope of the graph is rise / run and therefore represents change in position / change in clock time.

Change in position / change in clock time is by definition average velocity.

Conclusion:  The slope of a position vs. clock time graph between two points represents average velocity between those points.

7.  Sketch a possible graph of velocity vs. clock time for the situation of #5. 

• What property of the graph represents the change in velocity and what property represents the change in clock time?

The change in clock time is represented by the run of the graph between two points, and the change in velocity by the rise.

• What property of the graph represents the average acceleration between the two given points?

The slope of the graph is rise / run and therefore represents change in velocity / change in clock time.

Change in velocity / change in clock time is by definition average acceleration.

Conclusion:  The slope of a velocity vs. clock time graph between two points represents average acceleration between those points.

Using T = .2 sqrt(L) find the period of your pendulum, then determine how long it took the ball to roll down the incline.

The incline is 120 cm long.  Find the average velocity of the ball on the incline.

Assuming uniform acceleration sketch a v vs. t graph and find its slope.

period of pendulum, time to roll down incline, ave velocity, slope of v vs. t