A car covers the first half of the distance between two places at a speed of `40 kmh^(-1)` and second half at `60 kmh^(-1)` Calculate the average speed of the car.

Options

A. `40 kmh^(-1)`
B. `48 kmh^(-1)`
C. `50 kmh^(-1)`
D. `60 kmh^(-1)`

Answer

B

Explanation

As from the question,

Averages speed of the car `upsilon_(av)` is given by
`("Total distance travelled by the body(d)")/("Total time taken" (t_(1)+t_(2)))` ….(i)
So, now time taken in 1st half of the distance,
`t_(1)="Time"=("Distance")/("Vel,ocity")=(d)/(2xx40)`
(`therefore` distance `=(d)/(2)`, velocity = `40 kmh^(-1)`)
`rArr t_(1)=(d)/(80)`
Time takne for 2nd half, `t_(2)=(d)/(2xx"velocity")`
(`therefore` distance = `(d)/(2)` , velocity `= 60 kmh^(-1)`)
So, `t_(2)=(d)/(2xx60)=(d)/(120)`
Now, average velocity, `upsilon_(av)=(d)/((d)/(80)+(d)/(120))` [From Eq. (i)]
`=(dxx80xx120)/(200d)=48kmh^(-1)`