Is it true that the greater the mass the greater the kinetic energy and relationship between potential energy kinetic energy and speed?
No, it is not always true, it depends instead on what have you fixed as a constant.
For example, if you keep velocity constant, body with greater mass will definitely have greater kinetic energy, where in case overkeeping momentum of as the particle of object fixed, object with greater mass with have in act lower kinetic energy.
To be exact:
Kinetic energy of any object can also be expressed as square of momentum divided by twice of mass.
Relationship between KE and U(potential energy) depends on cases again, as generalized sense we can say total energy of particle is always equal to sum of potential and kinetic energy, ignoring other form of energy (confinement energy, binding energy, mass energy et cetera).
KE is equal to half of mass times square of speed.
In some cases, as in rotational motion, a yet much relationship between KE and PE be formed.
i.e.: KE= -PE/2
Anytime matter is in motion it has kinetic energy. The faster an object moves, the more kinetic energy it has. The more mass an object has, the more kinetic energy it has. The greater the mass, the greater the kinetic energy. So a body with greater mass does not possess less kinetic energy than another body of smaller mass moving with the same speed. Kinetic energy is directly proportional to the mass's product and the velocity square. So, by changing the velocity, a greater change in the kinetic energy of a body is caused. Because of this, a change in velocity affects kinetic energy more than a change in body mass. Also, kinetic energy is proportional to the square of velocity hence; lighter body has greater kinetic energy. It is obivious that doubling the velocity has a greater effect on the kinetic energy of a body than doubling its mass. More specifically, a more massive object will require more work in order to get from rest to a velocity v , and consequently have a higher kinetic energy, than a lighter object that goes from rest to the same velocity v. Potential energy is position relative. In other words, it changes depending on an object's height or distance and the mass of the object. Kinetic energy changes depending on an object's speed and it’s mass. If we think about a waterfall, some still water at the top of the waterfall has potential energy. Take the example of book sitting on a counter. When the book is at rest, it has potential energy. But, say, when a person walks by and accidentally knocks the book off of the counter, the book has kinetic energy as it falls, because it is in motion and the potential energy has transformed into kinetic energy. As the skater's speed increases, the kinetic energy increases. As the speed decreases, the kinetic energy increases. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters. Notice that gravitational potential energy has the same units as kinetic energy, kg m2 / s2.