Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 month ago

# physics homework?

A car is moving at 32 miles per hour. The

kinetic energy of that car is 5 × 10^5 J.

How much energy does the same car have

when it moves at 101 miles per hour?

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• Given,

Speed (v₁) = 32miles per hour = 14.3m/sec

Kinetic Energy (K.E₁) = 5 x 10⁵J

Kinetic Energy (K.E₂) = ?

Speed (v₂) = 101 miles per hour = 45.2m/sec

We know that:-

Kinetic Energy (K.E₁) = 1/2mv²₁

5 x 10⁵J = ½ x m x (14.3m/sec)²

10 x 10⁵J = m x (204.49m²/sec²)

Mass (m) = 10 x 10⁵ / 204.49 = 4890kg

Now, Kinetic Energy (K.E₂) = 1/2 mv₂²

= 1/2 x 4890 x (45.2m/sec)²

= 4.99 x 10⁶J.

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• v1 = first velocity of car = 32 mph = 14.30528 m/s

v2 = second velocity of car = 101 mph = 45.15104 m/s

KE1 = first kinetic energy = 5.00E+05 J

m = mass of car = to be determined

KE2 = second kinetic energy = to be determined

KE1 = 0.5 x m x v1²

KE1 / (0.5 x v1²) = m

m = KE1 / (0.5 x v1²)

m = 5.00E+05 J / [0.5 x (14.3 m/s)²]

m = 4,886.6 kg

KE2 = 0.5 x m x v2²

KE2 = 0.5 x 4,889.6 kg x (45.2 m/s)²

KE2 = 4.98E+06 J

Kinetic Energy Ratio = KE2 / KE1 = 9.96

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• We know ½*m*32² = 500,000 J = 5e5 J

½*m = 500,000/32²

½*m*101² = 500,000*101²/32² = 49.8e5 or about 50e5 J so the kinetic energy is nearly 10 times at 32mph

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• Anonymous
1 month ago

(101/32)^2 * 5 * 10^5 J

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