Physics Chapter: Motion in One Dimension
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Questions and Answers

What is the relationship between acceleration and mass for a constant force?

  • Acceleration is independent of mass.
  • Acceleration is directly proportional to mass.
  • Acceleration is equal to mass.
  • Acceleration is inversely proportional to mass. (correct)
  • What does the slope of a velocity vs. time graph represent?

  • Velocity
  • Displacement
  • Acceleration (correct)
  • Time
  • If an object has a constant acceleration, what can be said about its velocity?

  • Velocity is constant.
  • Velocity is increasing exponentially.
  • Velocity is decreasing linearly.
  • Velocity is increasing linearly. (correct)
  • The formula 'v(t) = vi + at' is derived from what relationship?

    <p>The relationship between velocity and time. (D)</p> Signup and view all the answers

    What does the area under the curve of a velocity vs. time graph represent?

    <p>Displacement (D)</p> Signup and view all the answers

    What is the significance of the y-intercept in the formula 'v = vi + at'?

    <p>The initial velocity (D)</p> Signup and view all the answers

    If the acceleration of an object is negative, what does this indicate about its motion?

    <p>The object is moving in the positive direction and slowing down. (A), The object is moving in the negative direction and speeding up. (C)</p> Signup and view all the answers

    Which of the following is NOT a feature of a velocity vs. time graph for an object with constant acceleration?

    <p>The graph is curved (C)</p> Signup and view all the answers

    A car travels 10 km east, then 5 km west, and finally 3 km east. What is the total distance traveled by the car?

    <p>18 km (C)</p> Signup and view all the answers

    A car travels 10 km east, then 5 km west, and finally 3 km east. What is the displacement of the car?

    <p>8 km east (A)</p> Signup and view all the answers

    You drive your car from your home to the grocery store, which is 5 km away. You then return home, taking the same route. What is your total displacement for the trip?

    <p>0 km (C)</p> Signup and view all the answers

    A runner completes a 10-kilometer race in 45 minutes. What is the runner's average speed in kilometers per hour?

    <p>22.2 km/h (D)</p> Signup and view all the answers

    A car travels 15 km east in 30 minutes, then 10 km west in 20 minutes. What is the car's average velocity over the entire trip, in kilometers per hour?

    <p>15 km/h east (B)</p> Signup and view all the answers

    A car travels 15 km east in 30 minutes, then 10 km west in 20 minutes. What is the car's average speed over the entire trip, in kilometers per hour?

    <p>30 km/h (B)</p> Signup and view all the answers

    A car travels at a constant speed of 60 km/h for 2 hours. What is the car's displacement?

    <p>Cannot be determined from the information given (B)</p> Signup and view all the answers

    What is the formula for instantaneous velocity?

    <p>$\lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$ (D)</p> Signup and view all the answers

    Which of the following pairs of quantities both represent scalar quantities?

    <p>Distance and speed (C)</p> Signup and view all the answers

    What is the average velocity of the athlete during the first half of the swim?

    <p>$\frac{L}{t_1}$ (B)</p> Signup and view all the answers

    What is the average velocity of the athlete during the second half of the swim?

    <p>$\frac{-L}{t_2}$ (C)</p> Signup and view all the answers

    What is the average velocity of the athlete during the round trip?

    <p>0 (B)</p> Signup and view all the answers

    What is the average speed of the athlete during the round trip?

    <p>$\frac{2L}{t_1 + t_2}$ (B)</p> Signup and view all the answers

    Which of the following statements is TRUE about acceleration?

    <p>Acceleration is the time rate of change in velocity. (B)</p> Signup and view all the answers

    Which of these are factors that can cause acceleration?

    <p>All of the above (D)</p> Signup and view all the answers

    What is the main difference between speed and velocity?

    <p>All of the above (D)</p> Signup and view all the answers

    Given an initial velocity ($v_i$), a final velocity ($v_f$), and a constant acceleration ($a$), which of the following equations can be used to calculate the displacement ($x - x_i$)?

    <p>$x - x_i = \frac{1}{2} (v_i + v_f) t$ (C)</p> Signup and view all the answers

    If a body is moving with constant acceleration, what does the area under the velocity-time graph represent?

    <p>Displacement (D)</p> Signup and view all the answers

    What is the relationship between the displacement of an object and the area under its velocity-time graph for a constant acceleration?

    <p>They are equal (A)</p> Signup and view all the answers

    Which of the following quantities is directly proportional to the displacement of an object moving with constant acceleration?

    <p>Area under the velocity-time graph (A)</p> Signup and view all the answers

    Assume a body starts from rest. Which of the following scenarios will lead to the largest displacement after a certain time interval?

    <p>Constant acceleration of 2 m/s² (D)</p> Signup and view all the answers

    What is the key concept being applied in this scenario?

    <p>Kinematics (B)</p> Signup and view all the answers

    What is the primary reason why the author suggests avoiding the direct approach of looking for a formula?

    <p>It is more efficient to digest the context first and then apply appropriate formulas. (D)</p> Signup and view all the answers

    Which of the following steps is NOT explicitly mentioned in the text as a strategy for approaching the problem?

    <p>Apply the formula directly. (D)</p> Signup and view all the answers

    What does the symbol 'tr' represent in the equation '2R = 1/2 g(tr^2)'?

    <p>The time it takes for the red bead to reach point C. (B)</p> Signup and view all the answers

    What is the key difference between the accelerations of the red and blue beads?

    <p>The acceleration of the red bead is determined by the component of gravity acting along the incline, while the blue bead's acceleration is due to gravity alone. (D)</p> Signup and view all the answers

    What is the primary factor that influences the time it takes for the red bead to reach point C?

    <p>The angle of the incline (θ). (B)</p> Signup and view all the answers

    Considering the context, what does the term 'digest the question' refer to?

    <p>Understanding the question's meaning and the information it provides. (C)</p> Signup and view all the answers

    Based on the given information, which of the following assumptions can be made about the beads?

    <p>The beads are moving under the influence of gravity. (B)</p> Signup and view all the answers

    Which of the following correctly describes the relationship between the angle (\theta) and the angles (\alpha) and (\beta) in the text?

    <p>The angle (\theta) is the complement of both angles (\alpha) and (\beta). (D)</p> Signup and view all the answers

    Flashcards

    Distance

    Total length of the path traveled, regardless of direction.

    Displacement

    The change in position; final position minus initial position.

    Speed

    The total distance traveled divided by the total time taken.

    Velocity

    The total displacement divided by the total time taken, including direction.

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    Frame of Reference

    A coordinate system used to define position and motion.

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    Scalar Quantity

    A measurement that has only magnitude, not direction.

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    Vector Quantity

    A measurement that has both magnitude and direction.

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    Average Velocity

    The overall change in position divided by the total time taken.

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    Instantaneous Velocity

    The velocity of an object at a specific moment in time.

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    Average Speed

    Total distance traveled divided by the total time taken.

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    Acceleration

    Change in velocity over time, indicating how speed is changing.

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    Constant Acceleration

    When the velocity of an object changes at a constant rate over time.

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    Force and Acceleration

    A force must be present to produce acceleration.

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    Displacement vs Distance

    Displacement considers direction; distance does not.

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    Swimming Round Trip Analysis

    Average velocity can be zero if starting and ending points are the same.

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    Newton's 2nd Law

    The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass.

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    Velocity as a Function of Time

    Velocity changes linearly with time when acceleration is constant.

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    Acceleration Formula

    a = Δv / Δt, defines acceleration as the change in velocity over time.

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    Velocity Equation

    v(t) = vi + at; gives velocity at time t based on initial velocity and acceleration.

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    Velocity and Position Relation

    Velocity at time t can be used to find displacement over time: Δx = v(t') × Δt.

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    Graphical Representation of Acceleration

    A graph showing constant acceleration displays a horizontal line in the acceleration vs. time graph.

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    Initial Velocity

    The velocity of an object at the start of the observation period, denoted as vi.

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    Motion in One Dimension

    Movement along a straight line described by position changes over time.

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    Bead Problem

    A physics scenario involving beads sliding down a slope to test concepts of motion.

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    Acceleration due to gravity

    The rate at which an object speeds up as it falls, approximately 9.81 m/s² towards Earth.

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    Inclined Plane

    A flat surface tilted at an angle to the horizontal, affecting motion of objects.

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    Kinematic Equation

    A formula that relates displacement, velocity, acceleration, and time in linear motion.

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    Position vs. Time

    A graph representation that shows how an object's position changes over time.

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    Starting Conditions

    The initial state from which motion begins, including position and speed.

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    Unknown Variable

    A value not directly provided but needed to solve a problem, often represented by a symbol.

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    Total Displacement Formula

    x - xi = vi t + (1/2) a t², used for constant acceleration.

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    Area under v-t graph

    Represents total displacement; includes rectangles and triangles.

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    Finding Displacement with vf

    Use vi, vf, and a to calculate x - xi when a is constant.

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    Velocity-Time Relationship

    Velocity graph's area gives total displacement.

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    Isosceles Triangle

    A triangle with at least two equal sides and angles.

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    Complementary Angles

    Two angles that add up to 90 degrees.

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    Maximum Height

    The highest point reached by an object in projectile motion.

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    Time of Flight

    The total time an object is in the air during projectile motion.

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    Equations of Motion

    Mathematical statements that describe the motion of an object.

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    Vertical Motion

    The motion of an object in the up or down direction under gravity.

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    Study Notes

    Motion in One Dimension

    • Definition of Distance and Displacement:

      • Location needs a frame of reference (e.g., coordinates)
      • Distance is the total path traveled, independent of direction
      • Displacement is the difference between final and initial positions (a vector)
    • Displacement and Distance Example:

      • Travel from Montreal to Toronto (500 km) and back to Montreal results in a distance of 1000 km and a displacement of 0 km.
    • Speed and Velocity:

      • Speed is a scalar, indicating the rate of distance traveled (average speed considers total time).
      • Velocity is a vector, measuring the rate of displacement (average velocity is total displacement over total time).
    • Instantaneous Velocity:

      • The instantaneous velocity is the limit of the average velocity as time approaches zero
    • Acceleration:

      • Acceleration is the change in velocity over time
      • Constant acceleration is a common assumption in introductory physics problems
    • Acceleration Problems:

      • Speed and velocity are functions of time.
      • In many situations, acceleration is constant over time
      • Acceleration requires a force (contact or non-contact).
      • Constant acceleration can be described graphically or using equations.

    Kinematic Equations

    • Equations for Constant Acceleration:

      • Equations link displacement, initial and final velocity, acceleration, and time.
      • The formulas are beneficial for understanding motion with constant acceleration.
    • Relationship Between Velocity and Acceleration:

      • With constant acceleration, velocity changes linearly over time.
      • The slope of a velocity-time graph represents acceleration
    • Determining Displacement from Velocity:

      • The area under a velocity-time graph gives the displacement over a given time period (this is also true with constant acceleration).
    • Solving Problems with Given Quantities:

      • Several equations can be used to solve 1-dimensional motion problems with known values.
      • Selecting the right formula is crucial for solving problems.

    Application of Kinematic Equations

    • Example Problem (Throwing a Stone):
      • Example involving initial velocity, height, and maximum height reached to determine time, and velocity at different points.
      • Shows how to apply 1-dimensional motion equations.

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    Description

    This quiz covers the essentials of motion in one dimension, focusing on the definitions of distance and displacement, the difference between speed and velocity, and the concept of acceleration. Additionally, it provides examples to clarify these concepts, making it suitable for introductory physics students.

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