Physics: Motion and Force

Equations:

• F = ma
• W = Fd, or F = W/d (Where d = displacement)
• W = Fd = ΔPE = mgΔh
• x = vt (where v = average velocity)
• v = x/t (average) (where x = displacement)
• speed = distance/time (average)
• acceleration = Δv/t (instantaneous) 
• F = G (m1 x m2)/r^2 
• fs ≤ μsFn
• fk = μkFn
• F = -kΔx

A vector has a magnitude and a direction; a scalar has a magnitude only. Changing the magnitude or direction of a vector creates a new vector. 

Types of vectors include displacement, velocity and acceleration.

Types of scalars include distance and speed.

Vectors can also be broken down into components:

Common triangles: the 3-4-5 triangle, and the 5-12-13 triangle

---

The speed and velocity of a moving object will have the same magnitude, but the displacement and distance of a trip taken by that object will not necessarily have the same magnitude. A meandering path from point A to point B (distance) will differ in magnitude from the shortest path from A to B (displacement). 

*Point to make: An object's velocity and acceleration need not be in the same direction. An object can be moving to the left while accelerating to the right. If an object's acceleration and velocity are in opposite directions, the object is hence slowing down. 

---

Uniformly Accelerated Motion and Linear Motion"

Equations: 

• x - xº = vºt + (1/2)at^2
• v - vº = at
• v^2 = vº^2 + 2a(x - xº)
• v = 1/2(v + vº) 
• This is average velocity

Since v = displacement/time, then finding the slope at point 1 for example, will illustrate that the velocity at point 1 is 1m/s

On a displacement vs time graph, the slope is velocity, and the area is meaningless. One a velocity vs time graph, the slope is acceleration and the area is displacement. 

The peak height of the projectile can be found by rearranging the equation: 

• v = (2gh)^(1/2)

If an object is thrown up and to the right or left at some angle, without counting air resistance, the object will go in a parabolic motion, where one side will be the mirror of the other. 

Mass = Amount of stuff 

Weight = gravitational force an object experience, which is related to the amount of stuff

The Law of Universal Gravitation: 

• F = G(m1 x m2/r^2) where G = 6.67 x 10^-11 m^3 kg^-1 s^-2

Hooke's Law: (Usually for springs)

• F = -kΔx (where k is a constant given to a given object)