How will you show that kinetic energy depends on the speed of an object?
Answers
Answer:
Kinetic energy is the energy an object has because of its motion.
If an object is to be accelerated, force must be applied. Applying a force requires work to be done. After work has been done, energy will be transferred to the object, and the object will be moving with a new constant speed. This energy transferred is known as kinetic energy, and it depends on the mass and speed achieved.
For mathematical proof, we can start by finding work done…Let F force is applied to move the object of mass m through a distance d along a surface by a force parallel to that surface to do W work
In physics, work is the energy transferred to or from an object via the application of force along a displacement
so W=F.d …. (1)
but F=m.a where a is the acceleration of the object
Replacing F in the equation 1 we get W=m.a.d ……..(2)
According to kinematic equations of motion, v2f=v2i+2.a.d where vf is the final velocity and vi is the initial velocity
Replacing a in equation 2 we get W=m.d.(v2f−v2i)/2.d
W=m.(v2f−v2i)/2
W=m.v2f/2−m.v2i/2
and this quantity m.v2/2 is called Kinetic Energy
KE=m.v2/2
Alternatively, one can say that the change in kinetic energy is equal to the net work done on an object or system.
W=KEf−KEi=ΔKE