# How do force and momentum relate?

According to Newton's first law of motion, force is rate of change of momentum. Mathematically

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Force and momentum are related through Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum. Mathematically, this relationship is expressed as F = Δp/Δt, where F is the force, Δp is the change in momentum, and Δt is the change in time. In simpler terms, when a force is applied to an object, it causes a change in the object's momentum. The greater the force applied or the longer the duration of the force, the greater the change in momentum will be. Additionally, momentum is a vector quantity, meaning it has both magnitude and direction, so the force applied also affects the direction of the object's momentum change.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- An astronaut with a mass of #95 kg# is floating in space. If the astronaut throws an object with a mass of #8 kg# at a speed of #3/8 m/s#, how much will his speed change by?
- An astronaut with a mass of #80 kg# is floating in space. If the astronaut throws an object with a mass of #11 kg# at a speed of #3/8 m/s#, how much will his speed change by?
- N bullets each of mass m are fired with a velocity v m/ s at the rate of n bullets per sec., upon a wall. If the bullets are completely stopped by the wall, the reaction offered by the wall to the bullets is?
- A ball with a mass of #6 kg # and velocity of #8 m/s# collides with a second ball with a mass of #5 kg# and velocity of #- 2 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?
- A ball with a mass of #7 kg# moving at #4 m/s# hits a still ball with a mass of #9 kg#. If the first ball stops moving, how fast is the second ball moving?

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