SCIENCE 1 Reading Notes Answers - Unit P01: Motion in One Dimension

Name: ___[ANSWERS]___ Unit B01 – Motion in One Dimension Reading Notes Directions: Read each section on the night it is assigned, with emphasis on answering the questions below. Do NOT do any examples (unless yo ...

Name: ___[ANSWERS]___ Unit B01 – Motion in One Dimension Reading Notes Directions: Read each section on the night it is assigned, with emphasis on answering the questions below. Do NOT do any examples (unless you really want)—we do those in class. Section 2-1: Reference Frames and Displacement Explain what “frame of reference” is in terms a junior-high student could understand. Explain the difference between “distance” and “displacement”. Explain what a vector is. Explain what a scalar is. What letter is the symbol for displacement used in mathematical equations? Distance is measured in what units? Displacement is measured in what units? [UNAUTHORIZED COPYING OR USE OF ANY PART OF THIS PAGE IS ILLEGAL] 1 Example: Consider the coordinate axes below. Each box represents 1 meter. Fred’s position is Point A, which is at (x = 3, y = –3). Mark this point. Fred walks 5 meters to the left, 5 meters up, and 5 meters to the right, arriving at point B. Mark point B and Fred’s path on the diagram. What distance did Fred travel? What is the distance between points A and B? What is Fred’s displacement from his original position? Section 2-2: Average Velocity Give a word-equation for average speed. Give a word-equation for average velocity. What is the difference between speed and velocity? [UNAUTHORIZED COPYING OR USE OF ANY PART OF THIS PAGE IS ILLEGAL] 2 What is the symbol for time? Time is measured in what units? What is the symbol for velocity? Velocity is measured in what units? How is “average” indicated on the symbol for velocity? What symbol represents the word “change”? What mathematical operation is used when finding “change Example: Consider the coordinate axes below. Each box represents 1 meter. Frank’s position is Point C, which is at (x = 4, y = 4). Mark this point. Frank walks down at a speed of 2 m/s for 4 seconds. He then immediately walks left 3 m/s for 3 seconds. He waits for 5 seconds, and then walks 1 m/s upward for 8 seconds and stops at point D. Plot point C, point D, and Frank’s path. During this time, what distance did Frank travel? What is the distance between points C and D? What is Frank’s displacement from his original position? What is Frank’s average speed during this time? What is Frank’s average velocity during this time? Originally, Frank waited for 5 seconds (below point D). If he wanted to make his average speed half as much, how long should he have waited? Explain your reasoning. Would this amount of wait-time have also halved his average velocity? Yes Section 2-3: Instantaneous Velocity Explain what “instantaneous velocity” is in the simplest terms possible. Make sure you point out the difference between this and “average velocity”. What does a speedometer in a car measure? (a) Average Speed (b) Average Velocity (c) Instantaneous Speed (d) Instantaneous Velocity Explain why. What two instruments in a car can be used to measure the car’s average speed during a long car trip? Explain how to use these instruments to calculate average speed. Section 2-4: Acceleration Write a word-equation for acceleration. What is the symbol for acceleration? Acceleration is measured in what units? Explain where the “square” in the units for acceleration comes from. Explain the difference between velocity and acceleration using the words “rate of change of”. Acceleration is a vector. Explain how to determine the direction of acceleration. Example: Each diagram shows a car’s position at one second intervals as it travels along a line in the same direction. The solid black car is the final position at time = 5 seconds. For each diagram, make a graph of position vs. time, and draw an arrow indicating the direction of velocity and an arrow for acceleration: Section 2-5: Motion at Constant Acceleration Write the equation for velocity as a function of time for constant acceleration. Write the equation for average velocity under constant acceleration. Write the equation for position as a function of time for constant acceleration. Write the equation that relates velocity, acceleration, and position (the “no time” equation). Identify every symbol that you used in the four equations above. Section 2-6: Solving Problems | Example: A runner finishes a 100-meter dash in 8 seconds. Determine his average speed. Example: A car can go from zero to 30 m/s in 2 seconds. Determine the car’s average acceleration. | Example: Another car can go from zero to 30 m/s in 3 s. How far does the car go while it accelerates? Example: The radius of Earth’s orbit is 1.5 ´ 1011 m. How fast does Earth move as it orbits the Sun? [ Section 2-7: Falling Objects What type of motion is free-fall? (a) Constant Position (b) Constant Velocity (c) Constant Acceleration (d) Changing Acceleration What does the µ symbol mean in the top paragraph on page 33 that states “d µ t2”? How is that different than the = symbol? Explain Figure 2-17 on page 33. Why does the paper fall differently than the ball in one case, but not in the other? What is the value of the acceleration of gravity on Earth’s surface? What symbol do we give this number? | | Example: A person throws a ball upward near the edge of a building as shown. Ignore air resistance. The first white dot is the position of the ball when it leaves the thrower’s hand. Each white dot after that represents the ball’s position every second after the ball leaves the thrower’s hand. In the table below, the time represents how many seconds after the ball leaves the thrower’s hand. Fill in the boxes representing the ball’s velocity at each time. When the ball is at we know for sure its velocity is Each second, the ball’s velocity The speed is almost the same as velocity, except Fill in the ball’s acceleration at each time. How does the ball’s acceleration vary with time [ Graphical Analysis of Linear Motion How can a curve be considered to have a slope? How can velocity at a certain time be found by looking at a position vs. time graph? How can the change in position between two times be found from a velocity vs. time graph? How can acceleration at a certain time be found by looking at a velocity vs. time graph? How can the change in velocity between two times be found from an acceleration vs. time graph? Example: Consider the following x vs. t graph. Estimate the velocity at: During what time intervals is the velocity positive? negative? During what time intervals is the acceleration positive? negative? zero? What is the object’s average velocity between 0 and 10 seconds? Example: Consider the following v vs. t graph. What is the acceleration at: t = 11 s? – How far, and in which direction, did the object travel: from t = During what time intervals is the object speeding up? slowing down? During what time intervals is the acceleration positive? negative? zero? If the object is at Draw an acceleration vs. time graph and a position vs. time graph (assuming the object starts at –5 m). Write the appropriate equation in each box next to the description: On an x vs. t graph, the slope is and the area under the graph is meaningless. On a v vs. t graph, the slope is and the area under the graph is On an a vs. t graph, the slope is and the area under the graph is Determine the sign of velocity and acceleration for each of the following diagrams: Which two pairs of graphs represent the same motion? A and G C and H [ Example Problem: A ball is dropped from the top of a 200 m tall building. It freely falls for 4 seconds; at time = 4 seconds, the ball reaches its terminal velocity. Determine the following: | The distance the ball travels in the first 4 seconds while it freely falls. The terminal velocity of the ball after 4 seconds of falling. | The total time it takes for the ball to reach the ground. Draw a graph of the distance the ball has traveled (downward) as a function of time.