A particle moving in straight line cover half the distance with speed `3 ms^-1`. The other half is covered in two equal time intervals with speed `4.5 ms^-1 and 7.5 ms^-1` respectively. The average speed of the particle during motion is

Options

A. `4 ms^(-1)`
B. `5 ms^(-1)`
C. `5.5 ms^(-1)`
D. `4.5 ms^(-1)`

Answer

a

Explanation

Time taken to cover OA`=((x/2))/(3)=(x)/(6)`

Since AB and BC are covered in equal time intervels say `t_2`
`:. 4.5 t_(2)+7.5t_(2)=(x)/(2)implies t_(2)=(x)/(24)`
`:.` Total time taken, `t=(x)/(6)+(x)/(24)+(x)/(24)=(x)/(4)`.
`:.` Average speed =`(x)/(x//4)=4 m//s`