Speed

Calculative Methods or Formulas 1) Speed. Speed ⇒

𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑻𝒊𝒎𝒆

Average Speed

𝑻𝒐𝒕𝒂𝒍 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑪𝒐𝒗𝒆𝒓𝒆𝒅 𝑻𝒐𝒕𝒂𝒍 𝑻𝒊𝒎𝒆 𝑻𝒂𝒌𝒆𝒏

2) Velocity. Velocity Velocity

𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑻𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅 𝒊𝒏 𝒂 𝑮𝒊𝒗𝒆𝒏 𝑫𝒊𝒓𝒆𝒄𝒕𝒊𝒐𝒏 𝑻𝒊𝒎𝒆 𝑻𝒂𝒌𝒆𝒏

or

𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝑻𝒊𝒎𝒆 𝑻𝒂𝒌𝒆𝒏

Average Velocity Average Velocity

𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑻𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅 𝑻𝒊𝒎𝒆 𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲+𝐅𝐢𝐧𝐚𝐥 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲 𝟐

( a=

𝐮+𝐯 𝟐

)

3) Acceleration. Acceleration Acceleration Acceleration

𝐂𝐡𝐚𝐧𝐠𝐞 𝐢𝐧 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲 𝐓𝐢𝐦𝐞 𝐓𝐚𝐤𝐞𝐧 𝐟𝐨𝐫 𝐂𝐡𝐚𝐧𝐠𝐞

or

𝐅𝐢𝐧𝐚𝐥 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲−𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐞𝐥𝐨𝐜𝐢𝐭𝐲 𝐓𝐢𝐦𝐞 𝐓𝐚𝐤𝐞𝐧 𝐅𝐨𝐫𝐜𝐞 𝐌𝐚𝐬𝐬

𝐅

( a= ) 𝐦

( a=

𝐯−𝐮 𝐭

)

4) Such Important Equations of Motion. 𝒗 = 𝒖 + 𝒂𝒕 𝟏 𝟐 𝒔 = 𝒖𝒕 + 𝒂𝒕 𝟐 𝒗𝟐 = 𝒖𝟐 + 𝟐𝒂𝒔 Where,

V= Final Velocity U=Initial Velocity S=Speed of Object A=Acceleration of Object T= Time

5) Uniform Circular Motion. V=

𝟐𝛑𝐫 𝐭

( v=Speed and t=Time )

6) Momentum. Momentum=Mass X Velocity ( P= mv ) Total Momentum Before Collision

=

Total Momentum After Collision

𝒎𝟏 𝒖𝟏 + 𝒎𝟐 𝒖𝟐 = 𝒎𝟏 𝒗𝟏 + 𝒎𝟐 𝒗𝟐

7) Force. Force= Mass X Acceleration ( F= m x a )

8) Universal Law of Gravitational Motion. F=G

𝒎𝟏 𝒎𝟐 𝒓𝟐

( G= 6.67 x𝟏𝟎−𝟏𝟏 N𝒎𝟐 𝒌𝒈−𝟐 )

9) Acceleration due to Gravity. g =G

𝑴 𝑹𝟐

( g = 9.8m𝒔−𝟐 )

10) Equation of Motion for Freefalling Bodies. 𝒗 = 𝒖 ± 𝒈𝒕 𝟏 𝟐 𝒉 = 𝒖𝒕 ± 𝒈𝒕 𝟐 𝒗𝟐 = 𝒖𝟐 ± 𝟐𝒈𝒉

11) Weight. Weight= Mass X Acceleration due to Gravity ( W= mg )

12) Pressure. Pressure =

𝑭𝒐𝒓𝒄𝒆 𝑨𝒓𝒆𝒂

13) Density. Density =

𝐌𝐚𝐬𝐬 𝐕𝐨𝐥𝐮𝐦𝐞

Relative Density =

𝐃𝐞𝐧𝐬𝐢𝐭𝐲 𝐨𝐟 𝐭𝐡𝐞 𝐒𝐮𝐛𝐬𝐭𝐞𝐚𝐧𝐜𝐞 𝐃𝐞𝐧𝐬𝐢𝐭𝐲 𝐨𝐟 𝐖𝐚𝐭𝐞𝐫

14) Work. Work = Force x Distance ( W= F x S )

15) “Work Done Against Gravity” or “Potential Energy” Work Done in Lifting a Body = Weight of Body X Vertical Distance W= mgh Where, W= Work Done m = Mass of the Body g = Acceleration due to Gravity h = Height through Which the Body is Lifted

16) Formula for Work done When Body Moves at an Angle to the Direction of Force. W= F𝐜𝐨𝐬 𝛉 x S Where, F= Force Applied 𝜽= Angle between the Direction of Force and Direction of Motion S= Distance Travelled

17) Kinetic Energy. 𝟏

Kinetic Energy= m𝒗𝟐 𝟐

Where,

M = Mass of Body V = Velocity of Body or Speed of Body

18) Power. Power = Or

𝑾𝒐𝒓𝒌 𝑫𝒐𝒏𝒆 𝑻𝒊𝒎𝒆 𝑻𝒂𝒌𝒆𝒏

Power =

( P=

𝑾 𝒕

𝐄𝐧𝐞𝐫𝐠𝐲 𝐂𝐨𝐧𝐬𝐮𝐦𝐞 𝐓𝐢𝐦𝐞 𝐓𝐚𝐤𝐞𝐧

) ( P=

𝑬 𝒕

)

19) Sound. Speed of Sound = Frequency x Wavelength Distance Travelled by Sound = Time Interval =

𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝑺𝒐𝒖𝒏𝒅 𝒙 𝑻𝒊𝒎𝒆 𝟐

𝟏 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚

Speed of Sound = Wavelength X Frequency

20) Time of Flight. “It is defined as the Total Time for Which the Projectile Remains in Air.” 𝟐𝒖 𝐬𝐢𝐧 𝜽 T= 𝒈

21) Maximum Height. 𝒖𝟐 𝒔𝒊𝒏𝟐 𝜽 H= 𝟐𝒈

22) Electric Current. Electric Current (I) =

𝑪𝒉𝒂𝒓𝒈𝒆(𝒒) 𝑻𝒊𝒎𝒆(𝒕)

𝒒

( I= ) 𝒕

23) Electric Potential. Electric Potential (V) =

𝑾𝒐𝒓𝒌 𝑫𝒐𝒏𝒆 (𝑾) 𝑪𝒉𝒂𝒓𝒈𝒆 (𝒒)

𝑾

( V= ) 𝒒

24) Resistance. Resistance (R) =

𝑬𝒍𝒆𝒄𝒕𝒓𝒊𝒄 𝑷𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍(𝑽) 𝑪𝒖𝒓𝒓𝒆𝒏𝒕(𝑰)

𝑽

( R= ) 𝑰

25) Series Formula. 𝑹𝒑 = 𝑹𝟏 +𝑹𝟐 +𝑹𝟑 …….

( R= Resistance )

26) Parallel Formula. 𝟏 𝟏 =+ 𝑹𝒑 𝑹𝟏

+

𝟏 𝑹𝟐

+

𝟏 𝑹𝟑

…….

27) Electrical Heat. Heat = 𝑰𝟐 𝑹𝒕 Where, I= Electric Current R= Resistance T= Time

( R= Resistance )

28) Electric Power. Power (P) = Electric Potential (V) x Current (I) Or, Power (P) =

𝑬𝒍𝒆𝒄𝒕𝒓𝒊𝒄 𝑷𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍(𝑽)𝟐

(𝑷=

𝑹𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆(𝑹)

(P=VI)

𝑽𝟐 𝑹

) or,

Power (P) = 𝑪𝒖𝒓𝒓𝒆𝒏𝒕(𝑰)𝟐 𝒙 𝑹𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆 (𝑹) (𝑷 = 𝑰𝟐 𝑹 )

29) Electrical Energy. Electric Energy (E) = Power (P) x Time (t)

( E= Pt )

30) Mirror Formula. 𝟏 𝒗

Where,

𝟏

𝟏

𝒖

𝒇

+ =

F = Focal Length U = Object Distance V = Image Distance

31) Linear Mirror Magnification. Mirror Magnification = Or,

𝒎=

𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑰𝒎𝒂𝒈𝒆 𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑶𝒃𝒋𝒆𝒄𝒕

𝒉𝒊 𝒉𝒐

=

−𝒗 𝒖

=

−𝑰𝒎𝒂𝒈𝒆 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑶𝒃𝒋𝒆𝒄𝒕 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆

32) Lens Formula. 𝟏 𝒗

𝟏

𝟏

𝒖

𝒇

− =

33) Linear lens Magnification. Mirror Magnification =

𝒎=

Or,

𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑰𝒎𝒂𝒈𝒆 𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝑶𝒃𝒋𝒆𝒄𝒕

𝒉𝒊 𝒉𝒐

=

=

𝑰𝒎𝒂𝒈𝒆 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑶𝒃𝒋𝒆𝒄𝒕 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆

𝒗 𝒖

34) Refractive Index. 𝐑𝐞𝐟𝐫𝐚𝐜𝐭𝐢𝐯𝐞 𝐈𝐧𝐝𝐞𝐱 (µ) =

𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝑳𝒊𝒈𝒉𝒕 𝒊𝒏 𝑽𝒂𝒄𝒖𝒖𝒎/𝑨𝒊𝒓 𝒄 = 𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝑳𝒊𝒈𝒉𝒕 𝑰𝒏 𝑮𝒊𝒗𝒆𝒏 𝑴𝒆𝒅𝒊𝒖𝒎 𝒏

35) Power of a lens. 𝑷𝒐𝒘𝒆𝒓 = 𝟏 𝑭𝒐𝒄𝒂𝒍 𝑳𝒆𝒏𝒈𝒕𝒉(𝒊𝒏 𝒎𝒆𝒕𝒆𝒓)

(𝑷 =

𝟏 𝒇(𝒊𝒏 𝒎𝒆𝒕𝒆𝒓)

)