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Assuming that the human body can survive a maximum continuous acceleration of 6.48 m/s², calculate the minimum time in which a space ship can accelerate from 0 m/s to 3.0 × 107 m/s, that is, to a velocity that is 10% the velocity of light.

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Final answer:

The minimum time required for a spaceship to accelerate from rest to 10% the speed of light at a maximum continuous acceleration of 6.48 m/s² is 4.6296 × 10⁶ seconds.

Step-by-step explanation:

To calculate the minimum time in which a space ship can accelerate from 0 m/s to 3.0 × 107 m/s at a maximum continuous acceleration of 6.48 m/s², we use the formula for constant acceleration:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Given that the initial velocity u is 0 m/s, the final velocity v is 3.0 × 107 m/s, and the acceleration a is 6.48 m/s², the formula simplifies to:

v = at

Rearranging to solve for time t, we get:

t = v / a

t = 3.0 × 107 m/s / 6.48 m/s²

t = 4.6296 × 106 seconds

Therefore, the minimum time required for the spaceship to reach 10% the velocity of light is 4.6296 × 106 seconds.

User Darren Findlay
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