To find the time it takes for the rocket to reach a speed of 1,000 m/s with an acceleration of 50 m/s², we can use the equation of motion:
V = V0 + at
where: V is the final velocity (1,000 m/s), V0 is the initial velocity (0 m/s, since the rocket starts from rest), a is the acceleration (50 m/s²), and t is the time we want to find.
Rearranging the equation, we have:
t = (V - V0) / a
Plugging in the given values:
t = (1,000 m/s - 0 m/s) / 50 m/s² = 1,000 m/s / 50 m/s² = 20 seconds
Therefore, it will take the rocket 20 seconds to reach a speed of 1,000 m/s.