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

[TR0JAN]

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?

 

[dmoravec]

$$s(t) = \frac {1}{2} at^2 + v_ot +s_o$$ 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

 

[TR0JAN]

Thank you. I forgot about that equation. The answer is 65 seconds if anyone was interested.