$A$ sphere is suspended by a thread of length $\ell$. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension point?

What can be said about the law of conservation of energy?

$A$ uniform chain of mass $M$ and length $L$ is released from rest from a smooth horizontal surface as shown in the figure. The velocity of the chain at the instant it completely comes off the table will be:

Brakes stop a train in a distance $x$. If the braking force is reduced to one-fourth of its original value,what distance will the train travel before coming to a stop?

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $A$,the net work done on the block is

The energy required to accelerate a car from $10 \ m/s$ to $20 \ m/s$ is how many times the energy required to accelerate the same car from rest to $10 \ m/s$?