Chapter 2: Describing Movement in One Dimension, 1-D Linear Kinematics
Conceptual Questions
2.1 Displacement
- Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Specifically identify each quantity in your example.
- Under what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and displacement are exactly the same?
2.2 Vectors, Scalars, and Coordinate Systems
- A student writes, “A runner has a speed of -3.5m/s.” What is wrong with the student’s statement? What has the student actually described? Explain.
- Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
- A weather forecast states that the temperature is predicted to be -5ºC the following day. Is this temperature a vector or a scalar quantity? Explain.
- &Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
- *Give a specific example of a vector, stating its magnitude, units, and direction.
- *What do vectors and scalars have in common? How do they differ?
- *Is it possible to add a scalar quantity to a vector quantity?
- *Is it possible for two vectors of different magnitudes to add to zero? Is it possible for three vectors of different magnitudes to add to zero? Explain.
Solution: no, yes - *When a 10,000-m runner competing on a 400-m track crosses the finish line, what is the runner’s net displacement? Can this displacement be zero? Explain.
Solution: zero, yes - *A vector has zero magnitude. Is it necessary to specify its direction? Explain.
- *Can a magnitude of a vector be negative?
Solution: no - *If two vectors are equal, what can you say about their components? What can you say about their magnitudes? What can you say about their directions?
Solution: equal, equal, the same - *Give an example of a nonzero vector that has a component of zero.
Solution: a unit vector of the x-axis - *Explain why a vector cannot have a component greater than its own magnitude.
- *If one of the two components of a vector is not zero, can the magnitude of the other vector component of this vector be zero?
Solution: yes - *If two vectors have the same magnitude, do their components have to be the same?
2.3 Time, Velocity, and Speed
- Give an example (but not one from the text) of a device used to measure time and identify what change in that device indicates a change in time.
- There is a distinction between average speed and the magnitude of average velocity. Give an example that illustrates the difference between these two quantities.
- Does a car’s odometer measure position or displacement? Does its speedometer measure speed or velocity?
- If you divide the total distance traveled on a car trip (as determined by the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the average velocity? Under what circumstances are these two quantities the same?
- How are instantaneous velocity and instantaneous speed related to one another? How do they differ?
2.4 Acceleration
- Is it possible for speed to be constant while acceleration is not zero? Give an example of such a situation.
- Is it possible for velocity to be constant while acceleration is not zero? Explain.
- Give an example in which velocity is zero yet acceleration is not.
- If a subway train is moving to the left (has a negative velocity) and then comes to a stop, what is the direction of its acceleration? Is the acceleration positive or negative?
- Plus and minus signs are used in one-dimensional motion to indicate direction. What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?
2.5 Motion with Constant Acceleration
- When analyzing the motion of a single object, what is the required number of known physical variables that are needed to solve for the unknown quantities using the kinematic equations?
- State two scenarios of the kinematics of a single object where three known quantities require two kinematic equations to solve for the unknowns.
2.6 Problem-Solving Basics for One-Dimensional Kinematics
- What information do you need in order to choose which equation or equations to use to solve a problem? Explain.
- What is the last thing you should do when solving a problem? Explain.
2.7 Falling Objects: Human Movement in the Vertical Direction
- What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down?
- An object that is thrown straight up falls back to Earth. This is one-dimensional motion.
(a) When is its velocity zero?
(b) Does its velocity change direction?
(c) Does the acceleration due to gravity have the same sign on the way up as on the way down? - Suppose you throw a rock nearly straight up at a coconut in a palm tree, and the rock misses on the way up but hits the coconut on the way down. Neglecting air resistance, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the coconut on the way up? Is it more likely to dislodge the coconut on the way up or down? Explain.
- If an object is thrown straight up and air resistance is negligible, then its speed when it returns to the starting point is the same as when it was released. If air resistance were not negligible, how would its speed upon return compare with its initial speed? How would the maximum height to which it rises be affected?
- The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration due to gravity being the same, how many times higher could a safe fall on the Moon be than on Earth (gravitational acceleration on the Moon is about 1/6 that of the Earth)?
- How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of [latex]g[/latex] on Earth)?