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🔋college physics i – introduction review

Meters/second²

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

Meters per second squared (m/s²) is a unit of acceleration, which measures the rate of change in velocity over time. It represents the amount of change in velocity (in meters per second) that occurs in one second. This unit is particularly relevant in the context of centripetal acceleration, which describes the acceleration experienced by an object moving in a circular path.

5 Must Know Facts For Your Next Test

  1. Meters per second squared (m/s²) is the standard unit for measuring centripetal acceleration, which is the acceleration experienced by an object moving in a circular path.
  2. Centripetal acceleration is directed towards the center of the circular path and is perpendicular to the object's velocity at any given point.
  3. The magnitude of centripetal acceleration is directly proportional to the square of the object's speed and inversely proportional to the radius of the circular path.
  4. Centripetal acceleration is a vector quantity, meaning it has both magnitude and direction, and is essential in understanding the dynamics of circular motion.
  5. The value of centripetal acceleration can be used to calculate the centripetal force acting on an object, which is the force responsible for the object's circular motion.

Review Questions

  • Explain how the unit of meters per second squared (m/s²) is used to measure centripetal acceleration.
    • The unit of meters per second squared (m/s²) is used to measure centripetal acceleration because it represents the rate of change in an object's velocity as it moves in a circular path. Centripetal acceleration is the acceleration directed towards the center of the circular path, and it is perpendicular to the object's velocity. The magnitude of centripetal acceleration is directly proportional to the square of the object's speed and inversely proportional to the radius of the circular path. This unit allows us to quantify the acceleration experienced by an object undergoing circular motion.
  • Describe the relationship between centripetal acceleration, centripetal force, and circular motion.
    • Centripetal acceleration, measured in m/s², is a crucial component in understanding circular motion. Centripetal force, the force directed towards the center of the circular path, is responsible for causing the object to move in a circular trajectory. The magnitude of centripetal acceleration is directly proportional to the centripetal force acting on the object and inversely proportional to the object's mass. This relationship is expressed in the formula: $a_c = F_c/m$, where $a_c$ is the centripetal acceleration, $F_c$ is the centripetal force, and $m$ is the mass of the object. The value of centripetal acceleration can be used to calculate the centripetal force required to maintain circular motion.
  • Analyze how changes in an object's speed and the radius of its circular path affect the magnitude of its centripetal acceleration.
    • The magnitude of centripetal acceleration, measured in m/s², is directly proportional to the square of the object's speed and inversely proportional to the radius of the circular path. This relationship is expressed in the formula: $a_c = v^2/r$, where $a_c$ is the centripetal acceleration, $v$ is the object's speed, and $r$ is the radius of the circular path. As the object's speed increases, the centripetal acceleration experienced by the object will increase quadratically. Conversely, as the radius of the circular path increases, the centripetal acceleration will decrease inversely. This means that for a given speed, a larger circular path will result in a lower centripetal acceleration, while a smaller circular path will result in a higher centripetal acceleration. Understanding this relationship is crucial in analyzing the dynamics of circular motion.