You are testing a new roller coaster ride in which a car of mass m moves around a vertical circle of radius R. In one test, the car starts at the bottom of the circle (point A) with initial kinetic energy Ki. When the car reaches the top of the circle (point B), its kinetic energy is Ki/4, and its gravitational potential energy has increased by Ki/2. What was the speed of the car at point A, in terms of g and R?

The initial velocity is 2.3

Explanation:

Suppose the speed of car at point A is u .

Its kinetic energy K = mu²

At point B , its kinetic energy = K

and its gravitational potential energy = K = m g h = 2 m g R

here height h = 2 R ( radius of circle )

From the principle of conservation of energy

m u² =   m u² + 2 m g R

m u² = 2 m g R

Therefore u = =  2.3

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.