A 128 kg astronaut and his equipment are initially at rest. To move forward with a velocity of 2.34 m/s, the astronaut fires a 532 N rocket in the backward direction. How long does the astronaut need to fire the rocket?

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Q: what speed  ?  will he be going after  35.0 m ?

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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”