Matter and Energy I
Formulas
Topic
Formulas
Conversion factors
1 mile = 1609 meters
1 ft = 30.48 cm
1 inch = 2.54 cm
1 gallon = 3.785 liters
Vectors
Vector A: Vector components Ax, Ay
𝐴𝑥=𝐴𝐶𝑜𝑠𝜃
𝐴𝑦=𝐴𝑠𝑖𝑛𝜃
Resultant vector
Rx=Ax+Bx+Cx+Dx+…
Ry=Ay+By+Cy+Dy+…
𝑅 = √𝑅𝑥2+𝑅𝑦2
𝜃=𝑡𝑎𝑛−1𝑅𝑦
𝑅𝑥
Operations with vectors
vector-scalar product: 𝑛(𝐴)=𝑛𝐴
Dot product: 𝐴∙ 𝐵 = [𝐴][𝐵]𝐶𝑜𝑠𝜃
Cross product: ([𝐴𝑥𝐵])=[𝐴][𝐵]𝑆𝑒𝑛𝜃
One-dimension motion with constant
acceleration
𝑋 = (𝑉0+𝑉𝑓
2)𝑡
𝑉𝑓=𝑉0+𝑎𝑡
𝑋 = 𝑉0𝑡+1
2𝑎𝑡2
𝑋 = 𝑉𝑓𝑡− 1
2𝑎𝑡2
2𝑎𝑥 =𝑉𝑓2−𝑉02
𝑉=𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
𝑡=𝑡𝑖𝑚𝑒
One-dimension motion: Free fall and vertical
throw
𝑌 = (𝑉0+𝑉𝑓
2)𝑡
