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?

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