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A vehicle travels half the distance (L) ...

A vehicle travels half the distance (L) with speed ` V_1` and the other half with speed ` V_2`, then its average speed is .

A

`v_1 + v_2/2`

B

`2v_1 + v_2/v_1 + v_2`

C

`2v_(1)v_2/v_1 + v_2`

D

`L(v_1 + v_2)/v_(1)v_(2)`

Text Solution

Verified by Experts

The correct Answer is:
(c )
Time taken to travel first half distance,
`t_1 = (L/2)/v_1 = L/(2v_1)`
Time taken to travel second half distance, `t_2 = (L/2)/v_2 = L/(2v_2)`
Total time taken = `t_1 + t_2 = L/(2v_1) + L/(2v_2)`
Average speed `= ("Total distance travelled")/("Total time taken")`
`= L/(L/(2v_1) + L/(2v_2)) = 1/(1/2[1/v_1 + 1/v_2]) = (2v_(1)v_(2))/(v_(2) + v_(1))`
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