Question

The kinetic energy of an object is 40 joules. If its speed is reduced to half its initial value then find its new kinetic energy?
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Answer 1

Answer:

The new kinetic energy is 10 J.

Explanation:

Given :

The kinetic energy of an object is 40 joules.

To find :

the new kinetic energy if its speed is reduced to half its initial value.

Solution :

The kinetic energy is the energy possessed by an object by virtue of its motion.

It's given by the expression :

KE = ½ mv²

where

m denotes the mass of the object

v denotes the velocity of the object

________________

From the expression,

$\tt KE \propto v^2$

Let the initial speed be 'v'

$\rm v_1 = v$

The speed is reduced to half it's initial value.

new velocity = v/2

$\rm v_2 = \dfrac{v}{2}$

Initial Kinetic energy = 40 J

Substituting,

$\sf \dfrac{KE_1}{KE_2} = (\dfrac{v_1}{v_2}) ^2 \\\\ \sf \dfrac{40}{KE_2} = (\dfrac{v}{\dfrac{v}{2}})^2 \\\\ \sf \dfrac{40}{KE_2} = 2^2 \\\\ \sf KE_2 = 40/4 \\\\ \sf KE_2 = 10 J$

Therefore the new kinetic energy is 10 J.

Answer 2

Given :

The kinetic energy of an object is 40 joules.

To find :

the new kinetic energy if its speed is reduced to half its initial value.

Solution :

The kinetic energy is the energy possessed by an object by virtue of its motion.

It's given by the expression :

KE = ½ mv²

where

m denotes the mass of the object

v denotes the velocity of the object

From the expression,

$\[KE \propto {v^2}\]$

$\[\frac{{K{E_1}}}{{K{E_2}}} = {\left( {\frac{{{v_1}}}{{{v_2}}}} \right)^2}\]$

Let the initial speed be 'v'

The speed is reduced to half it's initial value.

new velocity = v/2

Initial Kinetic energy = 40 J

thus,

$\[\frac{{K{E_1}}}{{K{E_2}}} = {\left( {\frac{{{v_1}}}{{{v_2}}}} \right)^2}\]$

$\[\frac{{40}}{{K{E_2}}} = {\left( {\frac{{{v_1}}}{{{v_1}/2}}} \right)^2}\]$

$\[K{E_2} = 10J\]$

Hence the new Kinetic energy is 10J.