Exercise: Time, Speed & Distance

Questions for: Velocity

A delivery drone departs from a warehouse, flies 20 km due east, delivers a package, and then immediately flies 20 km due west back to the same warehouse. The entire trip takes 40 minutes. What was the drone's average velocity for the entire trip?
A: 0 km/h
B: 30 km/h
C: 60 km/h
D: 120 km/h
Answer: A
Velocity is a vector quantity defined as the rate of change of displacement. Displacement is the net change in position from the starting point to the ending point, considering direction. The drone started at the warehouse and returned to the same warehouse. Therefore, the net displacement for the entire trip is zero. Average velocity = Total displacement / Total time = 0 km / 40 minutes = 0 km/h. Why others are wrong: A — B — This represents half of the average speed. C — This represents the drone's average *speed* for the entire trip (40 km total distance / (2/3) hour). D — This value is double the average speed, indicating a calculation error.
A high-speed train is traveling at a steady 200 km/h. During a specific segment of its journey, it navigates a continuous curve, maintaining this speed throughout the turn. Considering the train's motion during this curved segment, which of the following statements is most accurate?
A: The train's speed is constant, and its velocity is constant.
B: The train's speed is changing, but its velocity is constant.
C: The train's speed is constant, but its velocity is changing.
D: Both the train's speed and velocity are changing.
Answer: C
1. The scenario states the train is traveling at a "steady 200 km/h," which directly indicates that its speed (the magnitude of motion) is constant. 2. Velocity is a vector quantity, meaning it encompasses both magnitude (speed) and direction. 3. When the train "navigates a continuous curve," its direction of travel is continuously changing. 4. Therefore, even though the speed remains constant, the continuous change in direction means the train's velocity is continuously changing. Why others are wrong: A — Velocity is a vector quantity that includes direction; if the direction is changing, the velocity cannot be constant. B — The scenario explicitly states the train is at a "steady 200 km/h," indicating its speed is constant, not changing. D — The scenario explicitly states the train is at a "steady 200 km/h," indicating its speed is constant, not changing.
A rally car is driven around a perfectly circular track, maintaining an instantaneous speed of 100 km/h at all points. Considering the car's motion, which of the following statements is accurate?
A: The car's speed and velocity are both unchanging.
B: The car's speed is unchanging, but its velocity is continuously changing.
C: The car's velocity is unchanging, but its speed is continuously changing.
D: Both the car's speed and velocity are continuously changing.
Answer: B
Speed is a scalar quantity, representing only the magnitude of motion. The scenario explicitly states the car maintains an instantaneous speed of 100 km/h, meaning its speed is constant. Velocity is a vector quantity, representing both the magnitude (speed) and the direction of motion. As the car moves around a circular track, its direction of travel is continuously changing. Since velocity is defined by both magnitude and direction, a continuous change in direction implies a continuous change in velocity, even if the speed remains constant. Why others are wrong: A — Velocity changes because the car's direction of motion is continuously altering. C — The car's speed is stated as unchanging (100 km/h). D — The car's speed is stated as unchanging (100 km/h).
A car travels 100 kilometers due north in 2 hours. It then immediately turns around and travels 100 kilometers due south in another 2 hours. Which of the following accurately describes the car's average speed and average velocity over the entire 4-hour journey?
A: Both its average speed and average velocity are 0 km/h.
B: Its average speed is 50 km/h, and its average velocity is 0 km/h.
C: Its average speed is 0 km/h, and its average velocity is 50 km/h.
D: Both its average speed and average velocity are 50 km/h.
Answer: B
1. Average speed is calculated by dividing the total distance traveled by the total time taken. 2. The total distance traveled is 100 km (north) + 100 km (south) = 200 km. 3. The total time taken for the journey is 2 hours + 2 hours = 4 hours. 4. Therefore, the average speed is 200 km / 4 hours = 50 km/h. 5. Average velocity is calculated by dividing the total displacement by the total time taken. 6. Displacement is the net change in position from the starting point to the ending point. 7. The car starts at a certain point, travels 100 km north, and then returns 100 km south, ending at its original starting position. 8. This means the total displacement of the car is 0 km. 9. Consequently, the average velocity is 0 km / 4 hours = 0 km/h. Why others are wrong: A — Incorrect, as the average speed is 50 km/h, not 0 km/h. B — Correct, as it accurately states the calculated average speed (50 km/h) and average velocity (0 km/h). C — Incorrect, as the average speed is 50 km/h (not 0 km/h) and the average velocity is 0 km/h (not 50 km/h). D — Incorrect, as the average velocity is 0 km/h, not 50 km/h.
A race car maintains a steady 200 km/h as it navigates a perfectly circular track. Which of the following statements regarding the car's motion is accurate?
A: The car's speed is constant, but its velocity is constantly changing.
B: Both the car's speed and velocity are constant.
C: The car's speed is constantly changing, but its velocity is constant.
D: Both the car's speed and velocity are constantly changing.
Answer: A
Speed is a scalar quantity, representing only the magnitude of how fast an object is moving. Velocity is a vector quantity, which includes both magnitude (speed) and direction. In this scenario, the car maintains a steady speed of 200 km/h, meaning the magnitude of its motion is constant. However, because the car is moving on a circular track, its direction of travel is continuously changing. Therefore, while its speed is constant, its velocity (which includes direction) is constantly changing. Why others are wrong: A — This statement correctly distinguishes between constant speed and changing velocity due to directional change. B — Velocity cannot be constant because the car's direction is continuously changing as it moves in a circle. C — The scenario explicitly states the car maintains a "steady 200 km/h," indicating constant speed, not changing speed. D — The car's speed is stated as steady, so it is not constantly changing; only its velocity is changing due to direction.
Ad Slot (Above Pagination)
Quiz