Aparticle 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