A ball is thrown vertically upwards. Air resistance is negligible. What is the variation with time t of the kinetic energy Ek of the ball?

The kinetic energy (Ek) of an object is given by the equation Ek = 1/2mv^2, where m is the mass of the object and v is its velocity.

When a ball is thrown vertically upwards, its velocity decreases as it ascends due to the force of gravity. At the peak of its trajectory, its velocity is momentarily zero before it starts to descend and its velocity increases again.

Therefore, the kinetic energy of the ball decreases as it ascends, is momentarily zero at the peak of its trajectory, and then increases as it descends. This variation with time can be represented by a V-shaped graph, with the kinetic energy decreasing from the initial throw to the peak of the trajectory, and then increasing from the peak to when it hits the ground.

It's important to note that this is a simplified model and assumes that air resistance is negligible. In reality, air resistance would cause the kinetic energy to decrease more rapidly as the ball ascends and also as it descends.