Understanding the Concept
When an object moves in a circle at a constant speed, it still experiences acceleration. This is because its *velocity* is constantly changing. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. Even though the speed is constant, the direction of the object's motion is continuously changing as it moves in the circle. This change in direction results in acceleration, which is directed towards the center of the circle. This is called centripetal acceleration.
Formula
The magnitude of centripetal acceleration (a) is given by:
a = v² / r
where:
* v is the speed of the object
* r is the radius of the circular path
Calculation
1. Identify the given values:
* r = 5.0 meters
* v = 10 m/s
2. Plug the values into the formula:
a = (10 m/s)² / 5.0 m
3. Calculate the result:
a = 100 m²/s² / 5.0 m = 20 m/s²
Answer:
The magnitude of the acceleration of the object is 20 m/s².
