Question

derive a relation between kinetic energy and momentum 'p' of an object having mass m and velocity v

Answer 1

kinetic energy=(1÷2)mv×v
multiplying and dividing with m
kinetic energy=(m×m×v×v)÷2m
momentum=mv=p
p×p=m×m×v×v
kinetic energy =(p×p)÷2m
root of (2m×kinetic energy)=p

Answer 2

$\huge\bold{Answer :}$

We know that a Cricket Ball is much Heavier then a Tennis Ball. Suppose we throw a Cricket ball and a Tennis Ball, Both with the Same Velocity. It will be Found that More Force is required to stop the Cricket ball [ which has more mass ] and less force is required to stop the tennis ball [ which has less mass ].

$<b>We can conclude that force required to stop a moving body is directly proportional to its mass$

Now, if throw two cricket balls of same mass with different velocities, it will be found that more force would be required to stop that cricket ball which is moving with higher velocity and less force is required to the Stop the Cricket ball moving with lower velocity.

$<b>So, We can conclude that the Force required to stop a moving body is also directly proportional to its velocity$

Thus, The quantity of Motion ina body depends on the Mass and Velocity of the Body. This gives us the Term "Momentum" which is defined as the product of mass and Velocity of a body.

$<b>THUS, MOMENTUM = MASS × VELOCITY$

p = m × v.