the formula of centripital accelaration is v>2/r

Q:Why here is square of speed ?

The formula you mentioned for centripetal acceleration, a = v^2/r, does involve squaring the speed. This is because centripetal acceleration is the acceleration experienced by an object moving in a circular path and constantly changing its direction. Let's break down why the speed needs to be squared in this formula.

In circular motion, an object is constantly changing direction, which means it is constantly changing its velocity. Remember that velocity is a vector quantity, meaning it has both magnitude (which represents speed) and direction. As the object moves along the circular path, its direction is continuously changing, resulting in a non-zero acceleration called centripetal acceleration.

To determine the magnitude of centripetal acceleration, we need to consider two things: the object's speed and the radius of the circular path it is moving along. The centripetal acceleration is directly proportional to the square of the object's velocity and inversely proportional to the radius of the circular path.

By squaring the speed, we are essentially accounting for the fact that the tangential acceleration of the object is directly proportional to the square of its speed. In other words, the faster an object moves along a circular path, the greater its centripetal acceleration will be.

So, the formula a = v^2/r is a way to mathematically express the relationship between centripetal acceleration, speed, and radius. It allows us to calculate the magnitude of centripetal acceleration by taking the square of the speed and dividing it by the radius of the circular path.