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Chapter 2: Problem 78

\(\bullet\) You decide to take high-speed strobe light photos of your little dog Holly as she runs along. Figure 2.54 shows some of these photos. The strobe flashes at a uniform rate, which means that the time interval between adjacent images is the same in all the photos. For each case, sketch clear qualitative (no numbers) graphs of Holly's position as a function of time and her velocity as a function of time.

Short Answer

Expert verified
Graph Holly's position and velocity over time based on strobe photos: constant speed gives a diagonal position line and a flat velocity line; changing speed curves the position line and slopes the velocity line.

Step by step solution

01

Understanding the Problem

We need to draw qualitative graphs of Holly's position and velocity over time based on high-speed strobe photos. The key point is that the photos are taken at equal time intervals, which indicates uniformity in data collection.
02

Analyzing Holly鈥檚 Motion

Observing the strobe photos, we determine if Holly moves with constant speed or if her speed changes over time. If the distance between successive images is the same, Holly's speed is constant. If the distance changes, her speed is changing.
03

Sketching the Position vs. Time Graph

Start drawing the graph with time as the horizontal axis and position as the vertical axis. If Holly's speed is constant, the graph is a straight diagonal line. If her speed changes, the graph will curve upwards or downwards depending on whether she speeds up or slows down respectively.
04

Sketching the Velocity vs. Time Graph

Now create a graph with time on the horizontal axis and velocity on the vertical axis. For constant speed, the graph is a horizontal line. If Holly's speed increases, the graph slopes upwards, and if her speed decreases, it slopes downwards.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Strobe Light Photography
Strobe light photography is a fascinating technique used to capture motion over time. It involves taking photos at short, equal intervals using a strobe light, which allows you to see how an object moves step by step.
Think of it as freezing time at regular points to observe motion in snapshots.
  • The strobe light flashes at a regular, uniform rate.
  • This creates a series of images, each taken at the same time difference from the last.
  • By examining these sequential photos, you can analyze how an object like a dog or a ball moves over time.
The key here is the uniformity. This regular timing means you can easily tell if your object is moving at a constant speed or not by simply looking at the distances between its positions in each photo.
Uniform Motion
Uniform motion is when an object moves at a constant speed in a straight line. It's predictable and straightforward because the rate of movement doesn't change.
Imagine a car driving on a highway at a steady speed of 60 mph without accelerating or slowing down, just like the consistent flashes of the strobe light.
  • In strobe light photos, if the object moves equal distances between each flash, it signifies uniform motion.
  • The position vs. time graph for uniform motion is a straight line, showing a constant slope. Such a line means that for every unit of time, the position changes by the same amount.
  • The velocity vs. time graph for uniform motion is a flat, horizontal line, demonstrating that the speed remains unchanged over time.
Whether it's Holly running at a constant pace or a train chugging along tracks, uniform motion means predictability in speed and no surprises.
Variable Motion
Variable motion occurs when an object's speed or direction changes over time. This kind of movement is more dynamic and often a bit more complex to analyze than uniform motion.
Consider Holly if she decides to sprint to fetch a ball; her speed would change as she starts running faster or slows down to a stop.
  • In the context of strobe light photography, if the images show varying distances between positions, it indicates variable motion.
  • The position vs. time graph for variable motion will be curved. An upward curve suggests acceleration, while a downward curve implies deceleration.
  • The velocity vs. time graph would have a slope. Positive slopes indicate speeding up, while negative slopes indicate slowing down.
Variable motion encompasses all sorts of real-world motion, like a plane taking off or a car braking at a red light. Understanding this type of motion helps in predicting and analyzing how speed and direction may change in various scenarios.

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Most popular questions from this chapter

An airplane travels 280 \(\mathrm{m}\) down the runway before taking off. Assuming that it has constant acceleration, if it starts from rest and becomes airborne in 8.00 s, how fast \((\) in \(\mathrm{m} / \mathrm{s})\) is it moving at takeoff?

A test driver at Incredible Motors, Inc., is testing a new model car having a speedometer calibrated to read m/s rather than mi/h. The following series of speedometer readings was obtained during a test run: $$\begin{array}{llllllllll}{\text { Time (s) }} & {0} & {2} & {4} & {6} & {8} & {10} & {12} & {14} & {16} \\ {\text { Velocity }(\mathrm{m} / \mathrm{s})} & {0} & {0} & {2} & {5} & {10} & {15} & {20} & {22} & {22}\end{array}$$ (a) Compute the average acceleration during each 2 s interval. Is the acceleration constant? Is it constant during any part of the test run? (b) Make a velocity-time graph of the data shown, using scales of \(1 \mathrm{cm}=1\) s horizontally and \(1 \mathrm{cm}=\) 2 \(\mathrm{m} / \mathrm{s}\) vertically. Draw a smooth curve through the plotted points. By measuring the slope of your curve, find the magnitude of the instantaneous acceleration at times \(t=9 \mathrm{s}, 13 \mathrm{s}\) and 15 \(\mathrm{s}\) .

Starting from rest, a boulder rolls down a hill with constant acceleration and travels 2.00 \(\mathrm{m}\) during the first second. (a) How far does it travel during the second second? (b) How fast is it moving at the end of the first second? at the end of the second second?

A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 \(\mathrm{m} / \mathrm{s}\) . Air resistance may be ignored. (a) At what time after being ejected is the boulder moving at 20.0 \(\mathrm{m} / \mathrm{s}\) upward? (b) At what time is it moving at 20.0 \(\mathrm{m} / \mathrm{s}\) downward? (c) When is the displacement of the boulder from its initial position zero? (d) When is the velocity of the boulder zero? (e) What are the magnitude and direction of the acceleration while the boulder is (i) moving upward? (ii) Moving downward? (iii) At the highest point? (f) Sketch \(a_{y}-t, v_{v}-t,\) and \(y-t\) graphs for the motion.

Earthquake waves. Earthquakes produce several types of shock waves. The best known are the P-waves (P for primary or pressure) and the S-waves (S for secondary or shear). In the earth's crust, P-waves travel at around 6.5 \(\mathrm{km} / \mathrm{s}\) while S-waves move at about 3.5 \(\mathrm{km} / \mathrm{s}\) . (The actual speeds vary with the type of material the waves are going through.) The time delay between the arrival of these two types of waves at a seismic recording station tells geologists how far away the earthquake that produced the waves occurred. (a) If the time delay at a seismic station is 33 s, how far from that station did the earthquake that produced the waves occurred. (a) If the time delay at a seismic station is 33 s, how far from that station did the earthquake occur? (b) One form of earthquake warning system detects the faster (but less damaging) P-waves and sounds an alarm when they first arrive, giving people a short time to seek cover before the more dangerous S-waves arrive. If an earthquake occurs 375 \(\mathrm{km}\) away from such a warning device, how much time would people have to take cover between the alarm and the arrival of the S-waves?
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