Question

A car drives one fourth of a road with u_1 the next fourth with u_2 the next with u_3 and the final with u_4. what is the average speed?

Answer 1

`V_(avg)=4/(1/u_1+1/u_2+1/u_3+1/u_4)`

Explanation:

Average velocity( `V_(avg)`) of the car is the ratio of total distance traveled to the total time taken .

Let total distance traveled be S. And `t_1,t_2,t_3,t_4` be the time taken to cover first,second ,third and final quatrain of distance.

From definition `V_(avg)=S/(t_1+t_2+t_3+t_4)`

Time taken to cover each quatrain is the distance traveled in that

interval time divided by the velocity with which the car cover that

distance in that interval .

From definition #t=(DISTANCE) /(VELOCITY) #

Distance traveled in each interval is the same and that is `S/4`

therefore `t_1=S/(4*u_1)`

`t_2=S/(4*u_2)`

`t_3=S/(4*u_3)`
`t_4=S/(4*u_4)`

now substituting tha values in the above equation

we get `V_(avg)=S/(S/(4*u_1)+S/(4*u_2)+S/(4*u_3)+S/(4*u_4))`
`V_(avg)=S/(S/4*(1/u_1+1/u_2+1/u_3+1/u_4)`
`color(red)(V_(avg)=4/(1/u_1+1/u_2+1/u_3+1/u_4))`