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CALCULUS-BASED PHYSICS ∆𝒙 𝒗= 𝒕 FORMULA AVERAGE VELOCITY UNIT CONVERSION...

CALCULUS-BASED PHYSICS ∆𝒙 𝒗= 𝒕 FORMULA AVERAGE VELOCITY UNIT CONVERSION *for distance 0.45 L = ___mL? 𝒅 1L = 1000mL – conversion factor 𝒗𝒂𝒗𝒆 = 𝒕 𝟏𝟎𝟎𝟎𝒎𝒍 where: 𝟎. 𝟒𝟓 𝑳 𝒙 = 𝟒𝟓𝟎𝒎𝒍 𝟏𝑳 d = distance travelled t = elapse time DISTANCE or *for displacement 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 = 𝑶𝑨 + 𝑶𝑩 𝜟𝒙 𝒙𝟐 − 𝒙𝟏 DISPLACEMENT 𝒗𝒂𝒗𝒈 = −= 𝜟𝒕 𝒕𝟐 − 𝒕𝟏 𝜟𝒙 = 𝒙𝟐 − 𝒙𝟏 AVERAGE SPEED where: 𝑻𝒐𝒕𝒂𝒍 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅 𝑺𝒂𝒗𝒈 = x1 = Initial position 𝜟𝒕 x2 = Final position ACCELERATION SPEED 𝒗𝟐 − 𝒗𝟏 ∆𝒗 𝒂𝒂𝒗𝒈 = = 𝒕𝟐 − 𝒕𝟏 ∆𝒕 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑻𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅 𝑺𝒑𝒆𝒆𝒅 = 𝑻𝒊𝒎𝒆 𝑻𝒂𝒌𝒆𝒏 where: VELOCITY 𝒗𝟐 = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝒗𝟏 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝐹𝑖𝑛𝑎𝑙 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 − 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛) ∆𝑣 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 ∆𝑡 = 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 or  CONSTANT ACCELERATION: A SPECIAL CASE FREE FALLING BODIES (UNIFORMLY ACCELERATED MOTION) 𝒗 = 𝒈𝒕 1.) 𝒅 = 𝒗𝒂𝒗𝒈 𝒕 𝟏 𝟐 𝒗𝒇 −𝒗𝒊 𝒉= 𝒈𝒕 2.) 𝒗 ̅= 𝟐 𝟐 𝒗𝒇 −𝒗𝒊 𝟐𝒉 3.) 𝒂 = 𝒕=√ 𝒕 𝒈 4.) 𝒗𝒇 𝟐 = 𝒗𝒊 𝟐 + 𝟐𝒂𝒅 𝒗 = √𝟐𝒈𝒉 𝟏 5.) 𝒅 = 𝒗𝒊 𝒕 + 𝟐 𝒂𝒕𝟐 where: v = velocity This formula: g = gravity (9.8 m/s2) 𝒗𝒇 − 𝒗𝒊 𝒂= h = height 𝒕 t = time can derived to: NEWTON’S LAW OF MOTION 𝒂𝒕 = 𝒗𝒇 − 𝒗𝒊 2ND LAW OF MOTION 𝒗𝒇 − 𝒗𝒊 𝒕= 𝒂 𝑽𝒇 = 𝑽𝒊 + 𝒂𝒕 𝑭 = 𝒎𝒂 𝑽𝒊 = 𝑽𝒇 − 𝒂𝒕 𝑭 𝒂= 𝒎 This formula: 𝒗𝒇 𝟐 = 𝒗𝒊 𝟐 + 𝟐𝒂𝒅 𝑭 𝒎= 𝒂 can derived to: 𝒗𝒇𝟐 − 𝒗𝒊𝟐 GRAVITATIONAL FORCE 𝒂= 𝟐𝒅 𝑭𝒈 = 𝒎𝒈 𝒗𝒇𝟐 − 𝒗𝒊𝟐 𝒅= 𝟐𝒂  THE NORMAL FORCE To find 𝑎 in the problem involving applied force and 𝑭𝑵 = 𝒎𝒂𝒚 + 𝒎𝒈 frictional force: or 𝑭𝑵 = 𝒎 (𝒈 + 𝒂𝒚 ) 𝑭𝒂𝒑𝒑 − 𝑭𝒇 𝒂= 𝒎 However, if the table and block is not accelerating relative to the ground then 𝒂𝒚 is = 0 and the TENSION equation for the normal force is 𝑭𝑵 = 𝒎𝒈 𝑭𝑻 = 𝒎 ( 𝒈 + 𝒂 ) COEFFICIENT OF FRICTION For two equation in two unknowns, a and T. Static Friction: Block B (which could be on a table or another surface, on a horizontal surface) Ff ≤ 𝝁 s FN 𝑭𝑩 = 𝑻 = 𝒎 𝑩 𝒂 Kinetic Friction: where: Ff = 𝝁 k FN 𝑚𝐵 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝐵𝑙𝑜𝑐𝑘 𝐵 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 where: 𝜇k = coefficient friction Block A (often the hanging mass, hanging FN = normal force vertically, subject to gravity.) Newton's second law applied to a scenario 𝑭𝑨 = 𝒎 𝑨 𝒈 − 𝑻 = 𝒎 𝑨 𝒂 involving applied force, frictional force, and where: the resulting acceleration of an object. 𝑚𝐴 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝐵𝑙𝑜𝑐𝑘 𝐴 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑭𝒂𝒑𝒑 − 𝑭𝒇 = 𝒎𝒂 𝑔 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 where: 𝐹𝑎𝑝𝑝 = 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒 To find the 𝑎 in two equation in two unknowns, a 𝐹𝑓 = 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒 and T: 𝑚 = 𝑚𝑎𝑠𝑠 𝒎𝑨 𝒈 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝒂= 𝒎𝑨 + 𝒎𝑩 where: 𝑚𝐴 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝐵𝑙𝑜𝑐𝑘 𝐴 𝑚𝐵 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝐵𝑙𝑜𝑐𝑘 𝐵 𝑔 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 BASAHIN N’YO PA RIN ANG MGA MODULE AT PPT, WALA NAMAN D’YAN ANG LAHAT NG SAGOT - jerickguyala