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A body of mass (m) moving along a straig...

A body of mass (m) moving along a straight line covers half the distance with a speed of ` 2 ms^(-1)` .
The remaining half of the distance is covered in two equal time intervals with a speed of ` 3 ms^(-1)` and ` 5 ms^(-2)` respectively.
The average speed of the particle for the entire journey is .

A

`3/8 ms^(-1)`

B

`8/3 ms^(-1)`

C

`4/3 ms^(-1)`

D

`16/3 ms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let 2S be the total distance travelled by the body .
Let `t_1` be the time taken by the body to travel first half of the distance .
`:. t_(1) = S/2`
Let `t_(2)` be the taken by the body for each time interval for the remaining half journey.
`:. S = 3t_(2) + 5t_(2) " or " t_(2) =S/8`
Average speed `= ("Total distance travelled ")/("Total time taken ")`
`=(2S)/(t_(1)+2t_(2))=(2S)/(S/2+2(S/8))=(2S)/(S/2+S/4)=8/3ms^(-1)`
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