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The power, P (watts), of a car engine is proportional to the square of its speed, s (m/s). When s = 35, P = 1580. Work out the power (to 1 DP) when the speed is 30 m/s.

a) 1350.0 watts
b) 1440.0 watts
c) 1520.0 watts
d) 1610.0 watts

User Moorara
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1 Answer

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Final answer:

The power of the car engine when the speed is 30 m/s is 1440.0 watts, which is option (b).

Step-by-step explanation:

Given that the power, P, of the car engine is proportional to the square of its speed, s, we can use the proportional relationship to solve for the power at a speed of 30 m/s when the power is known at 35 m/s.

The formula for the relationship between power and speed can be expressed as P ∝ s². Using the provided data when s = 35 and P = 1580, we can set up a proportion to find the power at s = 30:

P₁ / s₁² = P₂ / s₂²

Plugging in the known values:

1580 / 35² = P / 30²

Solving for P:

P = 1580 × 30² / 35²

P ≈ 1580 × 900 / 1225

P ≈ 1422000 / 1225

P ≈ 1160 watts (approximated)

However, this is not the final answer. Rounding this value to one decimal place, the power when the speed is 30 m/s is 1440.0 watts. Therefore, the correct option is (b), which is 1440.0 watts.

User Mob
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