How Long Does It Take Two Accelerating Objects to Meet in Space?

AI Thread Summary
To determine how long it takes for a space tug and an asteroid to meet, the astronauts apply a force of 490 N, resulting in different accelerations for both objects. The asteroid accelerates at 0.0803 m/s² while the tug accelerates at -0.149 m/s². Using the equation s(t) = (1/2)at² + v_ot + s_o, the time can be calculated based on initial speed, distance, and acceleration. After performing the calculations, it is concluded that the two objects will meet in 65 seconds. This scenario illustrates the application of physics principles in space dynamics.
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Here is the question:

Astronauts have connected a line between their 3280 kg space tug and a 6100 kg asteroid.
Using their ship's engine, they pull on the asteroid with a force of 490 N. Initially the tug and the asteroid are at rest, 490 m apart.
How much time does it take for the ship and the asteroid to meet?

-490N 490N
Tug(3280kg)-------><------Asteroid(6100kg)
490m

So Acceleration = Force/Mass

Acceleration for the asteroid is 490/6100 = .0803 m/s2
Acceleration for the tug is -490/3280 = -.149 m/s2

How do I calculate the time when given the initial speed, the distance between, and the acceleration of two objects?
 
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s(t) = \frac {1}{2} at^2 + v_ot +s_o will give you position s as a function of time with a being acceleration and v_o being initial velocity. It can be solved for t if you know all of the other components
 
Thank you. I forgot about that equation. The answer is 65 seconds if anyone was interested.
 
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