3.1 Position, Displacement, and Average Velocity
Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Identify each quantity in your example specifically.
Under what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and distance are exactly the same?
Bacteria move back and forth using their flagella (structures that look like little tails). Speeds of up to 50 μm/s (50 × 10−6 m/s) have been observed. The total distance traveled by a bacterium is large for its size, whereas its displacement is small. Why is this?
Give an example of a device used to measure time and identify what change in that device indicates a change in time.
Does a car’s odometer measure distance traveled or displacement?
During a given time interval the average velocity of an object is zero. What can you conclude about its displacement over the time interval?
3.2 Instantaneous Velocity and Speed
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 the speedometer of a car measure speed or velocity?
If you divide the total distance traveled on a car trip (as determined by the odometer) by the elapsed time of the trip, are you calculating average speed or magnitude of 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?
3.3 Average and Instantaneous Acceleration
Is it possible for speed to be constant while acceleration is not zero?
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?
3.4 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 single object where three known quantities require two kinematic equations to solve for the unknowns.
3.5 Free Fall
What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down? Assume there is no air resistance.
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 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 just misses the coconut on the way up but hits the coconut on the way down. Neglecting air resistance and the slight horizontal variation in motion to account for the hit and miss of the coconut, 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.
The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration from gravity being the same, how many times higher could a safe fall occur on the Moon than on Earth (gravitational acceleration on the Moon is about one-sixth that of the Earth)?
How many times higher could an astronaut jump on the Moon than on Earth if her takeoff speed is the same in both locations (gravitational acceleration on the Moon is about on-sixth of that on Earth)?
3.6 Finding Velocity and Displacement from Acceleration
When given the acceleration function, what additional information is needed to find the velocity function and position function?