An object moves with velocity of 20km/hr in the first 1/3rd of total distance and moves with 60km/hr in the second 1/3rd of total distance. What is average velocity up to 2/3 rd of total distance?

1 Answer
Jun 14, 2015

A car cover 1/3 distance with speed 20km/hr and 2/3 with 60km/hr. average speed is 30km/hr.

Explanation:

ArunrajuNaspuri
Assume total length=#L kilometers#
Average velocity=Total distance up to#2/3#part /Time up to #2/3#part
#V_(avg)=(d_1+d_2)/(t_1+t_2)# #" "color(blue)((1))#

where,
#v_1#=velocity up to #1/3#rd part =20 km/hr,

#t_1#=time taken for car up to #(1/3)^(rd)# part,

#d_1#=distance up to #(1/3)^(rd)# part =#L/3#kilometers

#v_2#=velocity from #(1/3)^(rd)#part to #(2/3)^(rd)#part=60km/hr,

#t_2#=time taken from #(1/3)^(rd)#part to #(2/3)^(rd)#part,

#d_2#=distance from #(1/3)^(rd)#part to #(2/3)^(rd)#part= #L/3#km.

For first #1/3#rd part:
given that,

#v_1=20(km)/(hr)#

#d_1/t_1=20#km/hr [since from velocity definition]

#L/3/t_1=20#km/hr [since#d_1=L/3#]

#L/(t_1)=60#km/hr #" "color(blue)((2))#

from #(1/3)^(rd)#part to #(2/3)^(rd)#part:

given that,

#v_2=60 #km/hr,

#d_2/t_2#=60km/hr,

#L/3/t_2#=60km/hr [since #d_2=L/3km#]

#L/(3t_2)#=60km/hr #" "color(blue)((3))#

Divide equation(2) with equation(1),

We get #t_1=3t_2# #" "color(blue)((4))#

From equation(1),

#V_(avg)=(d_1+d_2)/(t_1+t_2)#

#V_(avg)=((L/3)+(L/3))/(3(t_2)+t_2)#[since from equation(4)]

#V_(avg)=1/2*(L/(3t_2))#

#V_(avg)=1/2*(60(km)/(hr))#[since from equation (3)]

#V_(avg)=30(km)/(hr)#

A car cover 1/3 distance with speed 20km/hr and 2/3 with 60km/hr. average speed is #" "color(blue)30# km/hr.