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. 11.3
B. 13.3
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)`

= ` 72 xx 5//18 m s ^(-1)`
` 20 m s ^(-1)`
The velocity during its second half of journey
` (x/2)`
` 36 km h^(-1)`
` 36 xx 5/18 m s^(-1)`
` 10 m s ^(-1)`
timee taken to travel first half of distance
` (t_(2)) = t =(x//2)/20 = x/20s`
Total time taken , ` (T) = t_(1) + t_(2) = ( x/40 + x/20)` s
` ((x+2x)/40)s = (3x)/40 s`
` " Average velocity " = ("total displacement ")/("total time taken ")`
`(x/ ((3x)//40))) ms ^(-1) = 40 /3 m s^(-1)`
`13.33 m s^(-1)`
`13.3 ms^(-1)`