Question

A car travels from point A to point B, moving in the same direction but with a non-constant speed. The first half of the distance, the car travels with a speed v 1 â.The remaining part of the way, the car travels half the time with a speed v2 ââand half the time with a speed v3 ââ . What is the average speed over the entire journey?

Answer 1

Step-by-step explanation:

From A to B

distance traveled with velocity
`v_1` in time
`t_1`

`(d)/(2)=v_1t_1----1`

from B to C

distance traveled is 0.5 d with
`v_2` and
`v_3` velocity for half-half time

`(d)/(2)=(v_2t_2)/(2)+(v_3t_3)/(2)----2`

divide 1 and 2 we get

`(1)/(1)=(2v_1t_1)/(v_2t_2+v_3t_3)`

`(t_1)/(t_2)=(v_2+v_3)/(2v_1)`

Now average velocity is given by

`v_(avg)=(d)/(t_1+t_2)`

taking
`t_1` common

`v_(avg)=(2v_1t_1)/(t_1(1+(t_2)/(t_1)))`

`v_(avg)=(2v_1)/(1+(2v_1)/(v_2+v_3))`

`v_(avg)=(2v_1(v_2+v_3))/(2v_1+v_2+v_3)`