Question

the kinetic energy of an object of mass m moving with a velocity of 5 m/sec is 25 j .what will be its kinetic energy when its velocity is increasing by 5 times *

Answer 1

Answer:

Hence, kinetic energy = 25 × 4 = 100 J. (ii) If velocity is increased three times, then its kinetic energy becomes 9 times the original value, because it is proportional to the square of the velocity. Hence, kinetic energy = 25 × 9 = 225 J.

Answer 2

Corrected question:

• What is the the kinetic energy of an object of mass m moving with a velocity of 5 m/sec is 25 j What will be its kinetic energy when its velocity is increasing by 5 times.

Information given to us:

• Kinetic energy is of 25 J
• Velocity is 5 m/s

What we have to calculate:

• Kinetic energy when velocity of that object is increased by 5 times.

Using Formula:

• $\boxed{\sf{k \: = \: \dfrac{1}{2} mv {}^{2} }}$

Where,

• K denotes kinetic energy
• m denotes mass
• v denotes velocity

Evaluating values:

Old Kinetic energy:-

We have,

• Kinetic energy of 25 J

$: \longmapsto \: \sf{ 25 \: = \: \dfrac{1}{2} \times m \times 5 {}^{2} }$

★ Cross multiplying,

$: \longmapsto \: \sf{ 25 \times 2 \: = \: 1\times m \times 5 {}^{2} }$

$: \longmapsto \: \sf{ 50\: = \: 1\times m \times 5 \times 5 }$

$: \longmapsto \: \sf{ 50\: = \: 1\times m \times 25 }$

$: \longmapsto \: \sf{ 50\: = \: m \times 25 }$

$: \longmapsto \: \sf{ 50\: = \: 25m }$

$: \longmapsto \: \sf{ m \: = \: \dfrac{50}{25} }$

$: \longmapsto \: \sf{ m \: = \: \cancel{\dfrac{50}{25} }}$

$: \longmapsto \: \boxed{ \sf{ m \: = \: 2 }}$

Thus, mass is 2kg

New Kinetic energy:-

As velocity is increased by 5 times,

• Velocity = 5 × 5
• Velocity = 25 m/s

Information given:

• Mass is 2kg
• Velocity is 25 m/s

Using Formula:

• $\boxed{\sf{k \: = \: \dfrac{1}{2} mv {}^{2} }}$

Where,

• K denotes kinetic energy
• m denotes mass
• v denotes velocity

Evaluating the values:

$: \longmapsto \: { \sf{k inetic \: energy \: = \: \dfrac{1}{2} \times 2 \times 25 {}^{2} }}$

$: \longmapsto \: { \sf{kinetic \: energy \: = \: \dfrac{1}{ \cancel2} \times \cancel2 \times 25{}^{2} }}$

$: \longmapsto \: { \sf{kinetic \: energy \: = \: 25 {}^{2} }}$

$: \longmapsto \: { \sf{kinetic \: energy \: = \: 25 \times 25}}$

$: \longmapsto \: \boxed{ \sf{kinetic \: energy \: = \: 625}}$

Thus,

• Kinetic energy would be of 625 J when its velocity is increased by 5 times.