Question

1/2 x mass x velocity squared is the rule to calculate: *

Answer 1

Answer:

In classical mechanics, kinetic energy (KE) is equal to half of an object's mass (1/2*m) multiplied by the velocity squared. For example, if a an object with a mass of 10 kg (m = 10 kg) is moving at a velocity of 5 meters per second (v = 5 m/s), the kinetic energy is equal to 125 Joules, or (1/2 * 10 kg) * 5 m/s2.

Explanation:

Answer 2

1/2 x mass x velocity squared is the rule to calculate kinetic energy.

• The formula stated in this question, that is $\frac{1}{2} m.v^{2}$ is to calculate the kinetic energy of a particle in motion.
• Kinetic energy is the energy that is induced because of the motion of the body.
• To keep a body in motion, work is to be done on the body. The velocity of the body attained because of this work done is equal to the kinetic energy of the body.

Let us see how the kinetic energy equation given here is derived.

As told earlier, kinetic energy = work done on the body

$Work\:done=Force \times displacement$

$\therefore W = F.s$

As work is done on the body, its velocity will change.

Let, $u=initial \:velocity, \:\:v=final \:velocity$

As we know,

$v^{2}-a^{2}=2as$

(Here, $a=acceleration; \:s=displacement$)

$\therefore s = \frac{v^{2}-u^{2}}{2a}$

While $F=m.a$

Substituting the values of F and s in equation of W,

$W=m.a\:\frac{v^{2}-u^{2}}{2a}$

Thus, $W= \frac{1}{2}m( {v^{2}-u^{2})$

$u=0; if\:body\:is \:at \:rest\:initially$.

Thus, $W= \frac{1}{2}m\:{v^{2}} = K.E.$