To find the time it takes for the spaceship to reach a 1.2 km distant asteroid, we can use the equation of motion:
s = ut + (1/2)at^2
where: s = distance u = initial velocity a = acceleration t = time
Given: Initial velocity (u) = 0 m/s (since the spaceship starts from rest) Acceleration (a) = 150 m/s^2 Distance (s) = 1.2 km = 1200 m
Plugging in the values into the equation of motion, we have:
1200 = 0 + (1/2)(150)t^2
Simplifying the equation:
1200 = 75t^2
Dividing both sides by 75:
16 = t^2
Taking the square root of both sides:
t = √16
t = 4 seconds
Therefore, it will take approximately 4 seconds for the spaceship to reach the 1.2 km distant asteroid when accelerating at 150 m/s^2 from rest.