Question

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

Answer 1

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

speed of the rocket will reach to 0.9c

$v_f = 0.9* 3 * 10^8 = 2.7 * 10^8 m/s$

now by kinematics

$v_f = v_i + a*t$

$2.7 * 10^8 = 0 + 10*t$

$t = 2.7*10^7 s$

Part b)

distance traveled by it in above time

$d = v*t + \frac{1}{2}at^2$

$d = 0 + \frac{1}{2}*10*(2.7*10^7)^2$

$d = 3.645 * 10^{15} m$

so this is the distance covered by the object