Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion.

Displacement is the vector quantity that represents the change in position of an object, measured from the initial to the final position.

Distance is a scalar quantity that measures the total path length traveled, while displacement is a vector quantity that measures the shortest straight-line distance from the initial to the final position.

Velocity is the rate of change of displacement with respect to time, and it is a vector quantity.

Average velocity is calculated as the total displacement divided by the total time taken, given by the formula: $$v_{avg} = \frac{\text{displacement}}{\text{time}}$$ .

Acceleration is the rate of change of velocity with respect to time, and it can be positive (speeding up) or negative (slowing down).

Acceleration can be calculated using the formula: $$a = \frac{\text{change in velocity}}{\text{time}}$$ .

When velocity is positive and acceleration is negative, the object is slowing down.

The slope of a position-time graph represents the velocity of the object.

The velocity function is found by taking the derivative of the position function with respect to time.