Final answer:
To determine the time required for a rocket to reach a velocity of 400 m/s with an acceleration of 20 m/s², use the formula t = (v - u) / a. It takes the rocket 20 seconds to reach the desired velocity.
Step-by-step explanation:
To calculate how long it takes for a rocket to reach a velocity of 400 m/s when it accelerates at a rate of 20 m/s²,
you can use the formula for constant acceleration:
v = u + at
where v is the final velocity, u is the initial velocity (which is 0 m/s at launch), a is the acceleration, and t is the time.
The question provides v = 400 m/s and a = 20 m/s².
Since the rocket starts from rest, u is 0 m/s. Rearranging the formula to solve for t gives:
t = (v - u) / a
Plugging in the numbers:
t = (400 m/s - 0 m/s) / 20 m/s² = 20 seconds
Therefore, it will take the rocket 20 seconds to reach a velocity of 400 m/s given an acceleration of 20 m/s².