Question

If the momentum of a body is numerically equal to its kinetic energy, then speed of body is​

Answer 1

Answer:

Let, m be the mass of the body and v be the velocity of the body.  

Now, momentum of the body is

p=mv

Kinetic energy is

E=  

2

1

​  

mv  

2

 

As per given condition  

2

1

​  

mv  

2

=mv=x(say)

2

1

​  

mv  

2

=x

2m

1

​  

m  

2

v  

2

=x

2m

1

​  

x  

2

=x

x=2m

Now,

mv=2m

v=2 ms  

−1

Explanation:

Answer 2

Given - The momentum of a body is numerically equal to its kinetic energy

Find - Speed

Solution - The velocity of the body is 2 metres/second.

The momentum of the body is given by the formula = mass*velocity.

The kinetic energy of the body is given by the formula = 1/2*mass*velocity².

Equating the two as per the question.

mass*velocity = 1/2*mass*velocity²

Mass and velocity will be cancelled as they are present on both sides. Right Hand Side will have velocity remaining. Thus, we get

velocity = 2 metre/second.

Thus, the velocity of the body is 2 metres/second.