If a rocket with a mass of 2500 tons vertically accelerates at a rate of # 7/3 ms^(-2)#, how much power will the rocket have to exert to maintain its acceleration at 5 seconds?

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

The power is

To calculate the power exerted by the rocket, we use the formula for power:

Power = Force × Velocity

First, we need to find the force exerted by the rocket. We can use Newton's second law of motion:

Force = Mass × Acceleration

Given that the mass of the rocket is 2500 tons and the acceleration is 7/3 ms^(-2), we can calculate the force:

Force = 2500 tons × 7/3 ms^(-2)

Next, we convert tons to kilograms:

1 ton = 1000 kilograms

So, 2500 tons = 2500 × 1000 kilograms

Now, we calculate the force:

Force = 2500 × 1000 kilograms × 7/3 ms^(-2)

Now, we have the force exerted by the rocket. Next, we need to find the velocity of the rocket at 5 seconds using the equation of motion:

Velocity = Initial velocity + (Acceleration × Time)

Given that the initial velocity is 0 m/s and the acceleration is 7/3 ms^(-2), and the time is 5 seconds, we can calculate the velocity:

Velocity = 0 + (7/3 ms^(-2) × 5 seconds)

Now, we have the velocity of the rocket. Finally, we can calculate the power exerted by the rocket using the formula:

Power = Force × Velocity

Substitute the values we calculated:

Power = (Force) × (Velocity)

Now, calculate the power.