A new spacecraft is built with an engine that is able to produce constant acceleration of 1g, where g = gravity’s acceleration on earth = 10m/s^2. A) calculate how long it would take the starship to reach a velocity of 0.9c where c is the speed of light. B) calculate how far the spaceship would travel during this time and compare this to our nearest neighbor in space, Alpha Centauri

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aristocles aristocles · Answer 1 · 2018-09-27T03:06:40+02:00

given that acceleration due to gravity is g = 10 m/s^2

speed of the rocket will reach to 0.9c

[tex]v_f = 0.9* 3 * 10^8 = 2.7 * 10^8 m/s[/tex]

now by kinematics

[tex]v_f = v_i + a*t[/tex]

[tex]2.7 * 10^8 = 0 + 10*t[/tex]

[tex]t = 2.7*10^7 s[/tex]

Part b)

distance traveled by it in above time

[tex]d = v*t + \frac{1}{2}at^2[/tex]

[tex]d = 0 + \frac{1}{2}*10*(2.7*10^7)^2[/tex]

[tex]d = 3.645 * 10^{15} m[/tex]

so this is the distance covered by the object