Question

two cars A and B of same mass moving with the speed of 100kmh-1 and 120 km h -1 respectively. which of the two has greater kinetic energy And why? ​

Answer 1

Given :

• Mass of car A = Mass of car B

• Velocity of car A = 100 km/h

• Velocity of car B = 120 km/h

To find :

The greater kinetic energy possessed by which car.

Solution :

We know that ,

• The kinetic energy of a body is directly proportional to the mass of the body i.e, greater the mass of the body , greater is the kinetic energy.

$\bf{K.E \propto m}$

Where ,

• KE = Kinetic energy
• m = Mass of the body

• The kinetic energy of a body is directly proportional to the square of the velocity of the body i.e, greater the mass of the body , greater is the kinetic energy.

$\bf{K.E \propto v^{2}}$

Where :

• K.E = Kinetic energy
• v = Velocity

Hence with this concept , we get to know that the kinetic energy possessed by a body will be greater if the velocity of the body will be more .

Hence the car B has more kinetic energy than car A since it's velocity is more than that of car A.

Mathematically ,

Let the mass be constant here with value 1kg.

Kinetic energy of car A :

We know the formula for Kinetic energy of a body i.e,

$\bf{K.E = mv^{2}}$

Using the above equation and substituting the values in it, we get :

$:\implies \bf{K.E = 1 \times 100^{2}}$

$:\implies \bf{K.E = 100^{2}}$

$:\implies \bf{K.E = 10000}$

$\boxed{\therefore \bf{K.E = 10000\:J}}$

Hence the Kinetic energy of car A is 10000 J.

Kinetic energy of car B :

We know the formula for Kinetic energy of a body i.e,

$\bf{K.E = mv^{2}}$

Using the above equation and substituting the values in it, we get :

$:\implies \bf{K.E = 1 \times 120^{2}}$

$:\implies \bf{K.E = 120^{2}}$

$:\implies \bf{K.E = 14400}$

$\boxed{\therefore \bf{K.E = 14400\:J}}$

Hence the Kinetic energy of car B is 14400 J.

Thus the kinetic energy of car B is greater than car A

Answer 2

$\boxed{KE = mv²}$

$\\ \overbrace {\underbrace{ \dfrac{ Mass_1 =m}{</p><p>Speed_1 = 110 km/h}}} \: \: \: \: \: \: \: \overbrace {\underbrace{ \dfrac{ Mass_2 =m}{</p><p>Speed_2 = 120 km/h}}}$

$\rm{KE_1 = 10000m ~~ \: \: ~~~ \: \: ~~~~ KE_2=14400m}$

$\rm{Since, KE_2 > KE_1}$

$\\ \underline{ \sf Car \: \red{B}~ possesses~ greater ~Kinetic ~Energy~ than~ car \: \red{A}.}$