Average Speed in Various Cases, Physics, Basic Statistics

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Define Average Speed in Various Cases

(a) Particles covering different distances in different times say a particle covers s1 distance in time t1 ,s2 in time t2, s3 in time t3 and so on then average speed is

v = s1 + s2 + s3+……. /t1 + t2+ t3……. = s1 + s2+ s3+……/s1/v1 + s2/v2 + s3/v3+……

Special case

If s1 = s2 = s

v = 2s/s (1/v1 + 1/v2) = 2v1 v2/v1 + v2 (harmonic mean)

(b) Bodies moving with different speeds in different intervals of time a body moves with velocity v1 on time t1, v2 in time t2, v3 in time t3 and so on then

v = v1 t1 + v2 t2 + v3 t3 +….. /t1 + t2 + t3 +…..

Special case

if t1 = t2 = t3…..t (say) then

v = v1 + v2 + v3+….vn (arithmetic mean)

Units of speed or velocity me-1 in SI, cms-1 in CGS and fts-1 on FPS. Dimensional formula (LT-11)

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-2]

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