Energy — Question 10

Speed of first car = 15 km h^-1
Speed of second car = 30 km h^-1
Mass of both cars = m

Kinetic energy of first car (K₁) = $\dfrac{\text{1}}{\text{2}}$ x mv²

= $\dfrac{\text{1}}{\text{2}}$ x m x (15)²

= $\dfrac{\text{225}}{\text{2}}$ x m

= 112.5 m J

Kinetic energy of second car (K₂) = $\dfrac{\text{1}}{\text{2}}$ x mv²

= $\dfrac{\text{1}}{\text{2}}$ x m x (30)²

= $\dfrac{\text{900}}{\text{2}}$ x m

= 450 m J

Comparing the kinetic energy we get:

$\dfrac{\text{K}_1}{\text{K}_2} = \dfrac{\text{112.5 m}}{\text{450 m}} = \dfrac{\text{1}}{\text{4}}$

So Kinetic energy of first car (K₁) : Kinetic energy of second car (K₂) = 1 : 4.