Nokea
Marilyn is driving to a wedding. She drives 4 miles south before realizing that she left the gift at home. She makes a U-turn, returns home to pick up the gift, and sets out again driving south. This time, she drives 1 mile out of her way to pick up a friend. From there, they continue 5 miles more to the wedding. Which of these statements is true about Marilyn's trip?
- A. The displacement of her trip is 6 miles, and the distance traveled is 6 miles.
- B. The displacement of her trip is 14 miles, and the distance traveled is 14 miles.
- C. The displacement of her trip is 8 miles, and the distance traveled is 14 miles.
- D. The displacement of her trip is 6 miles, and the distance traveled is 14 miles.
Correct Answer: C
Rationale: Marilyn's displacement is calculated based on her final position relative to the starting point. She drives 1 mile to pick up her friend, then 5 miles more to the wedding, totaling 6 miles after returning to her home. So, the correct displacement is 8 miles south from her starting point (4 miles to the gift + 4 miles return + 1 mile to the friend + 5 miles to the wedding). The total distance traveled is 14 miles (adding all the distances). Choice A is incorrect because it miscalculates the displacement. Choice B is incorrect as it overestimates both the displacement and distance traveled. Choice D is incorrect as it underestimates the displacement.
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In open-channel flow, a critical property is the free surface, which refers to the:
- A. Interface between the liquid and the container walls
- B. Interface between the liquid and a surrounding gas
- C. Bottom of the channel
- D. Region of highest velocity within the liquid
Correct Answer: B
Rationale: The free surface in open-channel flow refers to the interface between the liquid and the surrounding gas, typically the atmosphere. This interface is critical as it determines the boundary between the liquid flow and the open environment. Option A is incorrect as it refers to the liquid-container wall interface, not the free surface. Option C is incorrect because it represents the bottom of the channel, not the free surface. Option D is incorrect as it describes the region of highest velocity within the liquid, not the free surface. Therefore, the correct choice is B.
Fluid dynamics is a subfield of fluid mechanics concerned with:
- A. Equilibrium properties of fluids at rest (Fluid Statics)
- B. The motion and behavior of fluids under various conditions
- C. Phase transitions of fluids between liquid, gas, and solid states
- D. Engineering applications of fluids (related but broader than fluid dynamics)
Correct Answer: B
Rationale: Fluid dynamics is the study of fluids in motion and their behavior under different conditions, including how they flow, mix, and interact with their surroundings. It focuses on the dynamic aspects of fluids rather than their static properties when at rest, which is the realm of fluid statics. Phase transitions of fluids between liquid, gas, and solid states are more related to thermodynamics than fluid dynamics. While engineering applications involve fluid dynamics, the field itself is more specialized in studying the movement and behavior of fluids.
Which conclusion can be drawn from Ohm's law?
- A. Voltage and current are inversely proportional when resistance is constant.
- B. The ratio of the potential difference between the ends of a conductor to current is a constant, R.
- C. Voltage is the amount of charge that passes through a point per second.
- D. Power (P) can be calculated by multiplying current (I) by voltage (V).
Correct Answer: B
Rationale: Ohm's law states that the ratio of the potential difference (voltage) between the ends of a conductor to the current flowing through it is a constant. Mathematically, this is represented as V = I x R, where V is voltage, I is current, and R is the constant resistance. Therefore, the correct conclusion that can be drawn from Ohm's law is that the ratio of the potential difference between the ends of a conductor to current is a constant, denoted as R. This relationship is fundamental to understanding the behavior of electrical circuits and the effect of resistance on voltage and current. Choice A is incorrect because Ohm's law actually states that voltage and current are directly proportional when resistance is constant. Choice C is incorrect because voltage is not the amount of charge that passes through a point per second; rather, it is the electric potential energy per unit charge. Choice D is incorrect because although power (P) can be calculated by multiplying current (I) by voltage (V), this is not a conclusion directly drawn from Ohm's law.
What is the phenomenon by which light bends as it passes through a prism known as?
- A. Reflection
- B. Electrical conduction
- C. Diffraction
- D. Refraction
Correct Answer: D
Rationale: Refraction is the phenomenon by which light bends as it passes through a prism or any other medium boundary. When light transitions from one medium to another, such as air to glass in the case of a prism, it changes speed and direction due to the change in the medium's refractive index. This change in speed causes the light to bend. Reflection, on the other hand, is the bouncing back of light when it hits a surface. Diffraction refers to the bending of light around obstacles or through narrow openings. Electrical conduction involves the movement of electrically charged particles through a conductor, which is unrelated to the bending of light.
When calculating an object's acceleration, what must you do?
- A. Divide the change in time by the velocity.
- B. Multiply the velocity by the time.
- C. Find the difference between the time and velocity.
- D. Divide the change in velocity by the change in time.
Correct Answer: D
Rationale: When calculating an object's acceleration, you must divide the change in velocity by the change in time. Acceleration is defined as the rate of change of velocity with respect to time. By determining the ratio of the change in velocity to the change in time, you can ascertain how quickly the velocity of an object is changing, thereby finding its acceleration. Choice A is incorrect because acceleration is not calculated by dividing time by velocity. Choice B is incorrect as it describes multiplying velocity by time, which does not yield acceleration. Choice C is incorrect as finding the difference between time and velocity is not a method to calculate acceleration.