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29 June, 20:03

A particle travels rectilinearly a ceertain distance s. The particle travels half the distance (s/2) at a velocity v1. It travels the remaining distance (s/2) at a velocity v2 for half the time and a velocity v3 for the other half of the time.

1. What is the total time taken to travel the distance s?

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  1. 29 June, 23:56
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    s (2v₁+v₂+v₃) / 4

    Explanation:

    Recall that relationship between speed, distance and time is expressed as

    speed=distance/time.

    For the first part of the journey travelled at a speed of V₁ and covered a distance of (s/2), the time taken t₁ = (s/2) / v₁

    for the second part of the journey, let the time taken to complete both half of the second journey be t₂ and t₃ respectively. since it travel each half each distance at equal half time, then

    t₂₌t₃

    let the distance of the second journey be (s/2), where each time complete (s/4) distance. the time taken is

    t₂₌ (s/4) / v₂ and t₃ = (s/4) / v₃

    hence the total time taken is to cover the distance s is

    t=t₁+t₂+t₃

    t = (v₁s/2) + (v₂s/4) + (v₃s/4)

    t=s (2v₁+v₂+v₃) / 4
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