Hiya. First a comment from yesterday's class. I remarked that that the "area under the curve" for a v vs. t graph gives displacement. This is true - see the image from yesterday's class (in the previous blog post). The units of (v times t) gives units of displacement. For those of you who speak calculus, we refer to this area as an integral, a process made easier if you have a mathematical function that describes the velocity as a function of time.
If this makes no sense to you - fret not, physics friends. Simply know that the area under the curve gives you displacement.
And now, some problems to play with:
Woo Hoo – it’s physics problems with motion! OH YEAH!!!
1. Determine the average velocity of your own trip to school: in m/s and miles per hour.
2. Consider an echo-y canyon. You stand 200-m from the canyon wall. How long does it take the echo of your scream (“Arghhhh! Curse you Physics!!!”), if the speed of sound is 340 m/s? (Sound travels at a constant speed.)
3. What is the difference between traveling at an average speed of 65 mph for one hour and a constant speed of 65 mph for one hour? Will you go further in either case?
4. What is the meaning of instantaneous velocity? How can we measure it?
5. What is the acceleration of a toy car, moving from rest to 6 m/s in 4 seconds?
6. How far will a light pulse (say, a cell phone radio wave) travel in 10 minutes?
7. What does a negative acceleration indicate? How about a negative velocity? Negative displacement?
8. Consider an automobile starting from rest. It attains a speed of 30 m/s in 8 seconds. What is the car’s acceleration during this period, and how far has it traveled?
9. You are driving down a dark road when out pops a deer, 40 m away. Your speed is 20 m/s and you instantly slam on the brakes providing your car with a -2 m/s2 acceleration. Will you hit the deer? (Hint: Find out how far your car will travel given this acceleration, assuming that you come to a complete stop.)
10. What is the acceleration due to gravity? What does this value mean?
11. How does the acceleration due to gravity vary on the Moon? On Jupiter?
12. If you are “pulling 5 g’s”, what acceleration do you experience?
13. How long will it take a rock falling from rest to drop from a 100-m cliff?
14. If you drop a pebble from a bridge into a river below, and it takes 2.5 seconds to hit water, how high is the bridge?
15. Drop a bowling ball from atop a high platform. How fast will it be traveling after 3 seconds of freefall?
16. In order to pass another car on the highway, you increase your velocity from 25 m/s to 30 m/s. This occurs in 10 seconds. What is your acceleration? How far have you moved during this time?
17. You kick a soccer ball straight up into the air with an initial velocity of 22 m/s. How long will it take to reach apogee? To return to the Earth? How high will it rise? What will be its final velocity before hitting Earth?
18. Draw two (approximate) graphs of motion (displacement vs. time, velocity vs. time) for each of the following scenarios:
a. A car accelerates from rest for 5 seconds, travels at a constant velocity for 5 seconds, and then slows down for 5 seconds, finally stopping for 5 seconds.
b. A person walks at a constant velocity for 10 seconds, stops for 5 seconds, then walks back to where they started (faster) for 5 seconds.
c. You toss a ball up in the air and it lands back in your hand.
No comments:
Post a Comment