Equations Of Motion
Force = Mass * Acceleration
Average Speed = Total Distance Travelled / Total Time Taken
Velocity = Distance / Time
Average Speed = Total Distance Travelled / Total Time Taken
Average Velocity = Initial Velocity + Final Velocity / 2
Acceleration = Change In Velocity / Time Taken
Velocity = Initial Velocity + Acceleration * Time
Distance Travelled By The Object = Initial Velocity + 1/2(Acceleration*Time)
2 * Acceleration * Distance Travelled By The Object=(Final Velocity)2 - ( Initial Velocity )2
Algebraic Identities
(a + b)2 = a 2 + 2 ab + b 2
eg : (5x + 3)2 = (5x)2 + 2 (5x) (3) + (3)2
= 25x2 + 30 x + 9
= 25x2 + 30 x + 9
(a - b)2 = a 2 - 2 ab + b 2
eg : (2x - 3)2 = (2x)2 - 2 (2x) (3) + (3)2
= 4x2 - 12 x + 9
(a + b)3 = a 3 + 3 a2b + 3 ab2 + b 3
eg : (2x + 3)3 = (2x)3 + 3 (2x)2(3)+ 3 (2x)(3)2 + (3)3
= 23x3 + 3 (4x2)(3) + 3(2x)(9) + 27
= 8 x3 + 36 x 2 + 54 x + 27
(a 3 + b 3) = (a + b) (a 2 - ab + b 2)
eg : x3 + 2 3
= (x + 3) ((x)2 - x(3) + 3 2)
= (x+3) (x2 - 3x + 9)
(a 3 - b 3) = (a - b) (a 2 + ab + b 2)
eg : (5x)3 - 2 3
= (5x - 2) ((5x)2 + 5x(2) + 2 2 )
= (5x-2) (52x2 + 5x(2) + 22)
= (5x-2) (25x2 + 10x + 22)
(a 2 - b 2) = (a + b) (a - b)
eg :(5x)2 - 3 2
=(5x)2 - 32 = (5x + 3)(5x - 3)
(a 2 + b 2 + c 2) = a 2 + b 2 + c 2 + 2 ab + 2 bc + 2 ca
eg : (5x + 3y + 2z ) 2
= (5x)2 + (3y)2 + (2z)2 + 2 (5x) (3y) + 2 (3y) (2z) + 2 (2z) (5x)
= 52x2 + 32y2 + 22z2 + 2 (15 xy) + 2 (6yz) + 2 (10zx)
= 25x2 + 9y2 + 4z2 + 30 xy + 12yz + 20 zx
(x + a) (x + b) = x 2 + (a + b) x + ab
eg : (5x + 3y + 2z ) 2
= (5x)2 + (3y)2 + (2z)2 + 2 (5x) (3y) + 2 (3y) (2z) + 2 (2z) (5x)
= 52x2 + 32y2 + 22z2 + 2 (15 xy) + 2 (6yz) + 2 (10zx)
= 25x2 + 9y2 + 4z2 + 30 xy + 12yz + 20 zx
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