A 500kg spacecraft was traveling through space at a constant velocity when it fires its rocket engine. The engines produce a 1000N of thrust. The space craft was traveling at 400 m/s after 100 seconds.

(A)What is the rate of acceleration for the space craft?

(B)What was the speed of the space craft after 100 seconds?

(C) Later, the force of the thrust on the space craft doubled to 2000N. How would the acceleration be affected?

To find the answers to these questions, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

(A) The rate of acceleration for the spacecraft can be found using the formula:

acceleration = net force / mass

In this case, the net force is the thrust produced by the rocket engine, which is 1000N, and the mass of the spacecraft is 500kg.

acceleration = 1000N / 500kg

acceleration = 2 m/s²

So, the rate of acceleration for the spacecraft is 2 m/s².

(B) To find the speed of the spacecraft after 100 seconds, we need to use the formula:

final velocity = initial velocity + (acceleration × time)

In this case, the initial velocity is the speed of the spacecraft before firing the rocket engine, so it is given as 400 m/s. The acceleration is still 2 m/s², and the time is 100 seconds.

final velocity = 400 m/s + (2 m/s² × 100 s)

final velocity = 400 m/s + 200 m/s

final velocity = 600 m/s

So, the speed of the spacecraft after 100 seconds is 600 m/s.

(C) If the force of thrust is doubled to 2000N, the acceleration formula remains the same:

acceleration = net force / mass

However, in this case, the net force is now 2000N.

acceleration = 2000N / 500kg

acceleration = 4 m/s²

So, if the force of thrust is doubled to 2000N, the acceleration of the spacecraft would increase to 4 m/s².