A vechicle travels along a straight path between two places `alpha and beta`. It travels first half of the distance with a velocity of 72 km `h^(-1)` and the remaining distance with a velocity of 36 km `h^(-1)` then the average velocity of the vehicle is ______ m`s^(-1)`

Options

A. `11.bar3`
B. `13.bar3`
C. 15
D. 14

Answer

B

Explanation

Let the distance between `.alpha.and.beta.` be x m
The velocity during its first half of journey = 72 km `h^(-1)`

= `72xx5/18ms^(-1)`
= 20 `ms^(-1)`
The velocity during its second half of journey = `(x/2)`
= 36 km `h^(-1)`
= `36xx5/18ms^(-1)`
= 10 `ms^(-1)`
Time taken to travel first half of distance
`(t_(2))=t=(x/2)/20=x/40s`
Similarly, time taken to travel second half of the distance
`(t_(2))=(x/2)/10=x/20s`
Total time taken, (T) = `t_(1)+t_(2)=(x/40+x/20)s`
= `((x+2x)/40)s=(3x)/40s`
Average velocity = `("total displacement")/("total time taken")`
= `(x/((3x)/40))ms^(-1)=40/3ms^(-1)`
= `13.33ms^(-1)`
= `13.bar3ms^(-1)`