Exercise: Time, Speed & Distance
Questions for: Velocity
A car is traveling around a perfectly circular track at a steady rate of 50 km/h. Meanwhile, a second car is traveling in a straight line on a highway, also maintaining a steady rate of 50 km/h.
Which of the following statements accurately distinguishes the motion of the two cars?
A: Both cars exhibit constant velocity.
B: The first car has a changing velocity, while the second car has a constant velocity.
C: Both cars exhibit changing speed, but constant velocity.
D: The first car has a constant velocity, while the second car has a changing speed.
Answer: B
1. Velocity is a vector quantity, defined by both its magnitude (speed) and its direction.
2. The first car maintains a constant speed (50 km/h) but its direction is continuously changing as it moves around the circular track.
3. Because its direction is changing, the first car's velocity is not constant; it is continuously changing.
4. The second car maintains both a constant speed (50 km/h) and a constant direction (straight line).
5. Therefore, the second car's velocity is constant.
Why others are wrong:
A — Both cars cannot have constant velocity because the first car's direction is continuously changing, thus its velocity changes.
C — Both cars are described as maintaining a steady rate, meaning their speed is constant, not changing. The first car's velocity is also changing, not constant.
D — The first car's velocity is changing because its direction changes. The second car's speed is constant, not changing, as it maintains a steady rate.
An athlete runs multiple laps around a perfectly circular track, maintaining a constant pace throughout each lap.
Which of the following statements accurately describes the athlete's motion during a single lap?
A: The athlete's velocity remains constant because their speed does not change.
B: The athlete's velocity is continuously changing due to the constant alteration of direction.
C: The athlete's average velocity over one full lap is equal to their average speed.
D: D. The athlete's velocity is directed towards the center of the track at all times.
Answer: B
Velocity is a vector quantity, meaning it is defined by both its magnitude (speed) and its direction.
Even though the athlete maintains a constant pace (constant speed) on the circular track, their direction of motion is continuously changing at every point as they follow the curve.
Since velocity requires a constant direction to remain constant, and the direction is perpetually altering, the athlete's overall velocity is continuously changing.
Why others are wrong:
A — Velocity requires both constant speed AND constant direction; a change in direction alone means velocity changes.
C — Average velocity over a full lap is zero because the net displacement is zero, while average speed is non-zero (total distance divided by total time).
D — Velocity is always tangential to the circular path; the acceleration (specifically centripetal acceleration) is directed towards the center of the track.
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An aircraft completes a flight path, departing from Airport X, flying a designated route, and eventually landing back at Airport X. The total time taken for this flight was 3 hours, and the total distance covered was 1800 km.
Considering the entire flight from departure to landing, which statement accurately describes the aircraft's average velocity?
A: The average velocity was 600 km/h.
B: The average velocity was non-zero and dependent on the flight path.
C: The average velocity was 0 km/h.
D: The average velocity cannot be determined without knowing the aircraft's instantaneous speeds.
Answer: C
Velocity is a vector quantity defined as displacement over time.
Displacement is the straight-line distance and direction from the starting point to the ending point.
Since the aircraft departed from Airport X and landed back at Airport X, its total displacement is zero.
Average velocity is calculated as total displacement divided by total time.
Therefore, an average velocity of 0 km/h accurately describes the aircraft's entire journey.
Why others are wrong:
A — This value (1800 km / 3 h) represents the average speed, which is total distance divided by total time, not average velocity.
B — Average velocity is zero because the total displacement is zero, regardless of the flight path or any non-zero instantaneous velocities during the flight.
D — Average velocity can be determined using only the total displacement and total time; instantaneous speeds are not required for this calculation.
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A car travels along a perfectly circular racetrack, completing each lap in precisely the same amount of time.
Considering the car's motion, which of the following must be true?
A: Both the car's speed and its velocity are constant.
B: The car's speed is changing, but its velocity is constant.
C: The car's speed is constant, but its velocity is changing.
D: Both the car's speed and its velocity are changing.
Answer: C
The car completes each lap in the same amount of time, indicating it maintains a steady magnitude of motion, meaning its speed is constant.
Velocity is a vector quantity, encompassing both magnitude (speed) and direction.
For an object to travel along a circular path, its direction of motion must continuously change.
Since the car's direction is continuously changing, its velocity is also continuously changing, even though its speed remains constant.
Why others are wrong:
A — Velocity includes direction; a circular path means direction is constantly changing, so velocity cannot be constant.
B — The scenario describes a car completing laps in the same amount of time, which implies its speed (magnitude of velocity) is constant, not changing.
D — The scenario describes a car completing laps in the same amount of time, which implies its speed (magnitude of velocity) is constant, not changing.
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A satellite orbits Earth at a constant altitude, maintaining a steady speed of 28,000 km/h.
Which of the following statements accurately describes the satellite's motion?
A: Both its speed and its velocity are constant.
B: Its speed is constant, but its velocity is continuously changing.
C: Its speed is continuously changing, but its velocity is constant.
D: Both its speed and its velocity are continuously changing.
Answer: B
1. Velocity is a vector quantity, possessing both magnitude (speed) and direction.
2. Speed is a scalar quantity, representing only the magnitude of motion.
3. The scenario states the satellite maintains a "steady speed," indicating that its speed (magnitude of velocity) is constant.
4. However, as the satellite orbits Earth, its direction of travel is continuously changing to follow the curved path.
5. Since velocity includes direction, a continuous change in direction means the satellite's velocity is continuously changing, even if its speed remains constant.
Why others are wrong:
A — Incorrect because the satellite's direction of motion is continuously changing, meaning its velocity is not constant.
C — Incorrect because the scenario explicitly states the satellite maintains a "steady speed," not a continuously changing one.
D — Incorrect because the scenario explicitly states a "steady speed," making the speed constant, not continuously changing.
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