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Average Speed in Various Cases

**(a)**Particles covering different distances in different times say a particle covers

**s**

_{1}distance in time

**t**

_{1},s_{2}in time

**t**

_{2}, s_{3}in time

**t**and so on then average speed is

_{3}**v = s**

_{1}+ s_{2}+ s_{3}+……. /t_{1}+ t_{2}+ t_{3}……. = s_{1}+ s_{2}+ s_{3}+……/s_{1}/v_{1}+ s_{2}/v_{2}+ s_{3}/v_{3}+……Special case

If

**s**

_{1}= s_{2}= s**v = 2s/s (1/v**

_{1}+ 1/v_{2}) = 2v_{1}v_{2}/v1 + v_{2}(harmonic mean)**(b)**Bodies moving with different speeds in different intervals of time a body moves with velocity

**v**

_{1}on time

**t**

_{1},

**v**

_{2}in time

**t**

_{2},

**v**

_{3}in time

**t**and so on then

_{3}**v = v**

_{1}t_{1}+ v_{2}t_{2}+ v_{3}t_{3 }+….. /t_{1}+ t_{2 }+ t_{3}+…..**Special case**

if

**t**(say) then

_{1}= t_{2}= t_{3}…..t**v = v**(arithmetic mean)

_{1}+ v_{2}+ v_{3}+….v_{n}Units of speed or velocity

**me**

_{-1}in

**SI**,

**cms**

^{-1}in CGS and

**fts**

^{-1}on FPS. Dimensional formula (

**LT**

^{-1}1)Acceleration the time rate of change of velocity is called acceleration.

**A = dv/dt**

**(a)**Uniform acceleration a body is said to moves with uniform acceleration if acceleration remains constant throughout the motion and direction of motion does no change with time, that is,

**(i) A = dv/dt = constant**

**(ii)**Direction of motion remains unchanged.

**(b)**Variable or non-uniform acceleration if the acceleration is not constant or if the acceleration is constant but direction of motion varies or both vary. The particle is said to posses variable acceleration

Unit of acceleration

**ms**

^{-2}in SI system,

**cms**

^{-2 }in Cos system

**fts**

^{-2}FPS system

Dimensional formula of acceleration

**[LT**

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