Question

A 8.0 × 10⁴ kg spaceship is at rest in deep space. Its thrusters provide a force of 1200 kN. The spaceship fires its thrusters for 20 s, then coasts for 19 km. What is the final velocity of the spaceship?

Answer 1

The final velocity of the spaceship is calculated using Newton's second law to find the acceleration, and then applying this to determine the change in velocity over the time the thrusters are fired. With an initial velocity of 0 m/s, the final velocity after firing the thrusters for 20 seconds is 30 m/s.

Step-by-step explanation:

The question asks to calculate the final velocity of a spaceship given its mass, the force of its thrusters, the time the thrusters are fired, and the distance it coasts. Since the spaceship is initially at rest and acts under a constant force in deep space (where no friction or other forces act on it), we can make use of Newton's second law of motion to find the acceleration, and consequently use it to determine the final velocity after the thrusters have been fired.

First, calculate the acceleration (a) using:
a = F/m = 1200 kN / 8.0×10⁴ kg = (1200×10³ N) / (8.0×10⁴ kg) = 1.5 m/s²

Then, calculate the change in velocity (Δv) using the equation: Δv = a×t = 1.5 m/s² × 20 s = 30 m/s

Since the spaceship was initially at rest, the final velocity (v) is the same as the change in velocity: v = Δv = 30 m/s.