# If a rocket with a mass of #3500 "tons"# vertically accelerates at a rate of # 8/5 "m/s"^2#, how much power will the rocket have to exert to maintain its acceleration at 12 seconds?

The power is

According to Newton's second Law, the net force on the rocket is

The power is

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To find the power exerted by the rocket, you can use the equation: Power = Force × Velocity. First, calculate the force using Newton's second law: Force = mass × acceleration. Then, use the formula for power and substitute the calculated force and the given velocity (since velocity is the rate of change of displacement and is constant during vertical acceleration).

Given: Mass (m) = 3500 tons Acceleration (a) = 8/5 m/s^2 Time (t) = 12 seconds

Calculations: Force = mass × acceleration Force = 3500 tons × (8/5 m/s^2)

Convert tons to kilograms: 1 ton = 1000 kg Mass = 3500 tons × 1000 kg/ton Mass = 3,500,000 kg

Force = 3,500,000 kg × (8/5 m/s^2)

Force = 5,600,000 N

Power = Force × Velocity Power = 5,600,000 N × (8/5 m/s)

Power = 8,960,000 watts

Therefore, the rocket will have to exert approximately 8,960,000 watts of power to maintain its acceleration after 12 seconds.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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