If a rocket with a mass of #2500 tons # vertically accelerates at a rate of # 5/2 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 15 seconds?
The power is
According to Newton's second Law, the net force on the rocket is
The power is
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Power exerted by the rocket = Force × Velocity Force exerted by the rocket = Mass × Acceleration Force = (2500 tons) × (5/2 m/s^2) Velocity = Acceleration × Time = (5/2 m/s^2) × (15 s)
Calculate Force, then substitute into the power formula.My apologies for the oversight. To clarify, the correct formula for power (P) is:
[ P = \text{Force} \times \text{Velocity} ]
Given that force (F) is calculated as the product of mass (m) and acceleration (a):
[ F = m \times a ]
And velocity (v) is determined as the product of acceleration (a) and time (t):
[ v = a \times t ]
Now, substitute these values into the power formula:
[ P = (m \times a) \times (a \times t) ]
Plug in the provided values:
[ P = (2500 , \text{tons} \times \frac{5}{2} , \text{m/s}^2) \times \left(\frac{5}{2} , \text{m/s}^2 \times 15 , \text{s}\right) ]
Calculate to find the power exerted by the rocket.
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To calculate the power exerted by the rocket, we can use the formula:
[ P = F \cdot v ]
Where:
- ( P ) is the power,
- ( F ) is the force exerted by the rocket,
- ( v ) is the velocity of the rocket.
The force exerted by the rocket can be calculated using Newton's second law:
[ F = m \cdot a ]
Where:
- ( m ) is the mass of the rocket,
- ( a ) is the acceleration.
Given that the mass of the rocket is 2500 tons and the acceleration is ( \frac{5}{2} ) m/s², we can calculate the force:
[ F = 2500 , \text{tons} \times \frac{5}{2} , \text{m/s}^2 ]
Then, we need to convert the mass from tons to kilograms, where 1 ton = 1000 kg:
[ 2500 , \text{tons} = 2500 \times 1000 , \text{kg} ]
Now, we can calculate the force:
[ F = 2500 \times 1000 , \text{kg} \times \frac{5}{2} , \text{m/s}^2 ]
Next, we need to calculate the velocity of the rocket. Since the rocket is accelerating vertically, we'll use the formula:
[ v = u + at ]
Where:
- ( u ) is the initial velocity (which is typically 0 for objects starting from rest),
- ( a ) is the acceleration,
- ( t ) is the time.
Given that the rocket starts from rest, the initial velocity ( u = 0 ). So, we can calculate the final velocity using:
[ v = at ]
Substituting the values, ( a = \frac{5}{2} , \text{m/s}^2 ) and ( t = 15 ) seconds:
[ v = \frac{5}{2} , \text{m/s}^2 \times 15 , \text{seconds} ]
Now, we can calculate the power:
[ P = F \times v ]
Substitute the calculated values for force and velocity into the equation to find the power. Make sure to convert tons to kilograms before performing the calculations.
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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.
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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