Notes on Momentum and Impulse

Speed: Rate of motion; defined as the distance traveled per unit of time.
Velocity: The rate of change of position along a straight line with respect to time; includes direction.
Acceleration: Rate of change of velocity.
Mass: The amount of material in an object; contributes to its weight in a gravitational field.
Momentum (p): A measure of the motion of an object; defined as the product of mass and velocity. Formula:
p = mv
- Units: kg m/s
Impulse: Change in momentum; equal to force multiplied by the time over which the force acts. Formula:
I = F imes t
- Units: N·s

Impulse-Momentum Theorem: The impulse on an object equals the change in its momentum.
I = p
For an object not moving, the momentum is zero (if velocity = 0).

Sample Problem 1: Finding momentum of a bumper car with mass = 280 kg and velocity = 3.2 m/s.
p = mv = (280 ext{ kg})(3.2 ext{ m/s}) = 896 ext{ kg·m/s}
Sample Problem 2: Finding velocity of a bumper car with momentum = 675 kg·m/s and mass = 300 kg.
v = rac{p}{m} = rac{675 ext{ kg·m/s}}{300 ext{ kg}} = 2.25 ext{ m/s}
Sample Problem 3: Finding mass of a car with velocity = 20 m/s and momentum = 1500 kg·m/s.
m = rac{p}{v} = rac{1500 ext{ kg·m/s}}{20 ext{ m/s}} = 75 ext{ kg}

Understanding momentum and impulse is essential for analyzing collisions and other physical interactions in real-life situations.
Impulse can either increase or decrease an object's momentum, depending on the direction and magnitude of the applied force over time.
In collisions, the forces involved and the time of contact are crucial factors that influence the resulting changes in momentum and velocity.