Question

Represent K.E. in terms of momentum.
plz answer​

Answer 1

Answer:-

We know that:-

=> K.E. = 1/2mv²

Where:-

• K.E. is the kinetic energy of the body

• m is mass of the body

• v is velocity of the body

Now, from the above formula :-

=> K.E. = 1/2mv²×m/m

=> K.E. = (mv)²/2m. ----(1)

We know, the formula of momentum(p) :-

=> p = mv

By, putting the value of mv in eq.1, we get:-

=> K.E. = p²/2m

Thus, we can represent the relationship between kinetic energy and mimentum by the formula :- K.E. = p²/2m

Some Extra Information:-

• Kinetic energy is the energy possessed by a body beacause of it's motion.

• K.E. = 1/2mv²

Thus, K.E. of a body depends on 2 factors:-

(1) Mass [K.E. ∝ m]

(2) Velocity [K.E. ∝ v²]

• Kinetic energy of a body is always

positive. This is because mass can

never be negative and square of a real

value is always positive.

Answer 2

KE = Kinetic energy, p = momentum,

m = mass & v = final velocity.

$\sf KE = \dfrac{1}{2}mv²$

• $\sf \red{p = mv}$

$→\sf KE = \dfrac{1}{2}m×v×v$

$→\sf KE = \dfrac{1}{2}p×v$

$\star~{\boxed{\sf{KE = \frac{pv}{2} }}}$