Domanda del libro di testo
FIGURE EX5.14 shows an object's acceleration-versus-force graph. What is the object's mass?
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Ch 05: Force and Motion
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 5, Problema 10
For an object starting from rest and accelerating with constant acceleration, distance traveled is proportional to the square of the time. If an object travels 2.0 furlongs in the first 2.0 s, how far will it travel in the first 4.0 s?
Guida verificata passo dopo passo1
Step 1: Begin by recalling the kinematic equation for distance traveled under constant acceleration: , where 'd' is the distance, 'a' is the constant acceleration, and 't' is the time.
Step 2: Since the object starts from rest, the initial velocity is zero, and the distance traveled is proportional to the square of the time. This means doubling the time will result in a distance that is four times greater.
Step 3: Use the given information to determine the acceleration. Plug in the values for the first interval: furlongs and seconds. Rearrange the formula to solve for 'a': .
Step 4: Once the acceleration is determined, use the same kinematic equation to calculate the distance traveled in the first 4.0 seconds. Substitute seconds into the formula: .
Step 5: Simplify the equation to find the distance traveled in the first 4.0 seconds. Remember that the distance will be proportional to the square of the time, so the result should be four times the distance traveled in the first 2.0 seconds.
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Constant Acceleration
Constant acceleration refers to a situation where an object's velocity changes at a steady rate over time. In this context, it means that the object is accelerating uniformly, which allows us to use kinematic equations to predict its motion. This concept is crucial for understanding how distance, time, and acceleration relate to each other in linear motion.
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Kinematic Equations
Kinematic equations describe the motion of objects under constant acceleration. One key equation states that the distance traveled (s) is equal to the initial velocity (u) multiplied by time (t) plus half the acceleration (a) multiplied by the square of time (t²). This relationship allows us to calculate distances and times for objects in motion, particularly when starting from rest.
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Proportionality in Motion
In the context of uniformly accelerated motion, the distance traveled is proportional to the square of the time elapsed. This means that if the time doubles, the distance traveled increases by a factor of four, assuming constant acceleration. Understanding this proportionality is essential for solving problems related to distance and time in physics.
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