False Claim Response:
When an object is tossed vertically upward, its acceleration vector is constant. We observe that the velocity of the object is, at first, upward and decreasing in magnitude (speed). It stops momentarily when it reaches its maximum height, then speeds up as it heads back down toward the ground. Additionally, when carefully measured, it takes about the same time to go up to its maximum height as it takes to come down to its initial height. These observations are consistent with a constant, downward acceleration. Since acceleration is defined as a change in velocity, the evidence suggests an acceleration that is directed downward during the entire experiment. A downward acceleration on an upwardly moving object will slow it down, but once it stops at the maximum height, will speed it up while falling. Kinematic analysis using the maximum height and the time measurements can show that the acceleration has a constant magnitude and direction. All of this is consistent with the nature of gravity for positions close to the surface of the Earth where it produces a constant downward acceleration of 9.8 m/s2 on all masses.
Answers to Conceptual Questions:
1. Can the distance an object moves be the same as its displacement magnitude? If so, give an example.
Yes, when an object travels in a straight line in only one direction, the distance moved is equal to the magnitude of the displacement.
2. Your friend says that your car has a speed of -5 mph. How would you explain that he is wrong?
Speed is a scalar. It has no direction. So the negative sign has no meaning. In practice, the expression is sometimes used when the term velocity is actually correct. I make this mistake sometimes when I'm taking too fast!
3. Write down an example when the average speed and the magnitude of the average velocity are the same.
When an object undergoes a constant acceleration in one direction.
4. Explain how a negative acceleration can cause an object to speed up.
When an object is moving backward (relative to some FOR) and is speeding up.
5. Describe the physical condition needed to use the kinematic equations.
The acceleration must be constant.
6. If an object is tossed upward from the ground, and we assume free fall conditions, how does the time going upward compare to the time going downward? Assume the same start and finish point.
The time up will be the same as the time down. Interestingly, we will discuss the effect that air resistance plays in such a scenario in the next unit. We will find that the object takes longer to fall than to rise. Think about why that might be the case.
7. A friend tells you that its possible for an x-t graph of a real object to take the shape of a full circle. Besides the fact that the object would appear to move backward in time, make an argument proving that she is incorrect.
Claim: An x-t graph cannot form a full circle.
Evidence: At two points in the motion the object will have a vertical slope.
Justification: The magnitude of the slope on an x-t graph is the speed. A vertical slope means infinitely high speed...an impossibilty according to all the laws of physics.
8. Can a v-t graph shaped like the letter V ever indicate that the motion of an object is zero? How about that the acceleration of the object is zero?
The object can have a speed of zero at any point on a v-t graph depending upon where the time axis cuts through it. The acceleration can be zero only at the base of the V, where the slope is zero.
9. Can the area under a v-t graph ever, by itself, indicate where an object is positioned? Explain your response.
Without knowing the initial position of the object, the area under the v-t graph, by itself, can only give displacement. If the initial position is known, one can determine the final position with the help of the v-t graph.
10. Your classmate claims that accuracy and uncertainty are the same regarding measurements. Explain why he is wrong.
A measurement's accuracy is how close it is to the accepted value. Even though one may have an accurate measurement, that doesn't mean it is perfectly certain. All measurements have uncertainty based upon the quality of the device used and the skill of the person using the device. For example, if you need to measure the distance between two points marked on the ground, and the ruler you use is marked at each centimeter, the most certainty you could achieve is to the closest centimeter. Anything beyond that would be a guess. The tenths place is significant but not certain. If the marks are actually 7.92 cm apart, you would likely measure the distance as 7.9 cm +/- 0.1 cm. This could be considered accurate and have a low amount of uncertainty. If however, you used a ruler that only had a zero mark and a 10 cm mark, you would likely measure 8 cm +/- 1 cm as the reading. This is slightly less accurate, but the uncertainty is much larger.