# If a rocket with a mass of 3900 tons vertically accelerates at a rate of # 7/8 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 5 seconds?

##### 1 Answer

Approximately

#### Explanation:

We first find the net force acting on the rocket using Newton's second law of motion, which states that,

where:

#F_"net"# is the net force in newtons

#m# is the mass in kilograms

#a# is the acceleration in meters per second squared

Here, the net force is the force applied to the rocket by acceleration plus the rocket's weight.

Substituting our values, we get:

Now, we find the velocity of the rocket, given by the equation:

where:

#v# is the final velocity

#u# is the initial velocity

#a# is the acceleration

#t# is the time taken

Assuming

Power is given by the equation:

where:

#P# is the power in watts

#F# is the force in newtons

#v# is the velocity in meters per second

So, we get: