Question

if the kinetic energy and linear momentum of a body are equal, the velocity of the body is ​

Answer 1

Answer :

➥ The velocity of the body = 2 m/s

Given :

➤ The kinetic energy and linear momentum of a body are equal.

To Find :

➤ The velocity of the body = ?

Required Solution :

For solving this question, Let's first know about kinetic energy and linear momentum.

✒ Kinetic energy:

• The SI unit of kinetic energy is Joule.
• Kinetic energy is represented by K.E.
• Kinetic energy is defined as K.E = ½mv²

『Where, K.E is the kinetic energy, m is the mass and v is the velocity.』

✒ Linear momentum:

• The SI unit of linear momentum is kg m/s.
• Linear momentum is represented by p.
• Linear momentum is defined as p = mv.

『Where, p is the Linear momentum, m is the mass and v is the velocity.』

Let's solve this question...

❒ In the given question given that the kinetic energy and linear momentum of a body are equal that means kinetic energy is ½mv² and linear momentum is mv.

✎ So let's find Velocity of the body (v) !

Kinetic energy = Linear momentum

$\tt{: \implies } \dfrac{1}{2} \cancel{m}{v}^{2} = \cancel{m}v$

$\tt{: \implies \dfrac{1}{2} {v}^{2} = v}$

$\tt{: \implies \dfrac{1}{2}v = v}$

$\tt{: \implies \dfrac{1}{2}v = 1 }$

$\tt{: \implies v = 1 \div \dfrac{1}{2}}$

$\tt{: \implies v = 1 \times \dfrac{2}{1} }$

$\tt{: \implies v = \dfrac{2}{1} }$

$\bf{: \implies \underline{ \: \: \underline{ \red{ \: \: v = 2 \: m/s \: \: }} \: \: }}$

║Hence, the velocity of the body is 2 m/s.║

Answer 2

2m/s

Explanation:

K.E=P

K.E=1/2 mv²

P=mv

K.E=Pv/2

v/2=1

v=2m/s