Question

QUESTION 30... A car is running at
a speed of 15 kilometre per hour
while another car is moving at a
speed of 21 kilometre per hour. Their
kinetic energies are in the ratio
5:1
O 7:5
O 25:49
49:25​

Answer 1

ANSWER:

• The ratio of their kinetic energies = 25 : 49.

GIVEN:

• A car is running at a speed of 15 kmph

• Another car is moving at a speed of 21 kmph.

TO FIND:

• The ratio of their kinetic energies.

EXPLANATION:

$\boxed {\bold{ \large{ \gray{Kinetic\ Energy =\dfrac{1}{2} mv^2}}}}$

$\sf Let\ the\ velocity\ of\ first\ car\ be\ v_1$

$\sf Let\ the\ velocity\ of\ sevond\ car\ be\ v_2$

Assume massess of both cars be the same.

$\sf \dfrac{K.E_1}{K.E_2}=\dfrac{\dfrac{1}{2} mv_1^2}{\dfrac{1}{2} mv_2^2}$

$\sf \dfrac{K.E_1}{K.E_2}=\dfrac{v_1^2}{v_2^2}$

$\sf v_1 = 15\ kmph\ and\ v_2 = 21\ kmph$

$\sf \dfrac{K.E_1}{K.E_2}=\dfrac{15^2}{21^2}$

$\sf \dfrac{K.E_1}{K.E_2}=\dfrac{15 \times 15}{21 \times 21}$

$\sf \dfrac{K.E_1}{K.E_2}=\dfrac{5 \times 5}{7 \times 7}$

$\sf \dfrac{K.E_1}{K.E_2}=\dfrac{25}{49}$

HENCE THE RATIO OF KINETIC ENERGIES IS 25 : 49.

Additional Points:

• Every body will possess kinetic energy when it has non - zero velocity.

• When velocity is zero, kinetic energy will also be zero.

• It also means that when kinetic energy is zero velocity will be zero as mass of a body cannot be equal to zero. [ K.E = 1/2 mv² ]

• When K.E is zero, the body will possess potential energy.

• Total energy = kinetic energy + potential energy.

• Total energy is always constant.