Answer:
K.Eₓ = 4 K.E
K.Eₓ = 9 K.E
Explanation:
Th formula for the kinetic energy of a body is given as follows:
[tex]K.E = \frac{1}{2}mv^2\\[/tex] ---------------equation (1)
where,
K.E = Kinetic Energy of Automobile
m = mass of automobile
v = speed of automobile
For twice speed:
vₓ = 2v
then,
[tex]K.E_{x} = \frac{1}{2}mv_{x}^2\\K.E_{x} = \frac{1}{2}m(2v)^2\\K.E_{x} = 4\frac{1}{2}mv^2\\[/tex]
using equation (1):
K.Eₓ = 4 K.E
For thrice speed:
vₓ = 3v
then,
[tex]K.E_{x} = \frac{1}{2}mv_{x}^2\\K.E_{x} = \frac{1}{2}m(3v)^2\\K.E_{x} = 9\frac{1}{2}mv^2\\[/tex]
using equation (1):
K.Eₓ = 9 K.E
A. The kinetic energy of automobile when it moves at twice the speed is 8000 J
B. The kinetic energy of automobile when it moves at three times the speed is 18000 J
Let the mass of the automobile be constant.
Let the initial velocity be v
A. Determination of the kinetic energy of the automobile when it moves at twice the speed.
KE₁ /v₁² = KE₂ / v₂²
2000 / v² = KE₂ / (2v)²
2000 / v² = KE₂ / 4v²
Cancel out v²
2000 = KE₂ / 4
Cross multiply
KE₂ = 2000 × 4
KE₂ = 8000 J
B. Determination of the kinetic energy of the automobile when it moves at three times the speed.
KE₁ /v₁² = KE₂ / v₂²
2000 / v² = KE₂ / (3v)²
2000 / v² = KE₂ / 9v²
Cancel out v²
2000 = KE₂ / 9
Cross multiply
KE₂ = 2000 × 9
KE₂ = 18000 J
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