A particle moving in a straight line covers half the distance with a speed of `3 m s^(-1)`. The other half of the distance is covered in two equal time intervals with speeds of `4.5 m s^(-1)`, and `7. 5 m s^(-1)`, respectively. Find the average speed of the particle during this motion.

Options

A. ` 4.0m//s`
B. ` 5.0 m//s`
C. `5.5m//s`
D. ` 4.8 m//s`

Answer

A

Explanation

Let the total distance be S. Time taken to travel the first half ` ie.(S)/(2) is t_1 (S//2)/(3) = (S)/(6) `
Let `t_2` be the time taken to cover a distance `S_1` with speed 4.5 m/s and `t_3 `that cover distance
` 7.5 m//s . ` then ` S_1 =4.5 t_2 and S_2 = 7.5 t_3`
Now ` S_1 +S_2 =(S)/(2) and t_2 =t_3 " " ` (Given )
Therefore ` " "(S)/(2) =S_1 +S_2=( 4.5 + 7.5 )t_2 rarr t_2=(S)/(24) " "therefore " "` Total time taken ` t_1+2t_2 =(S)/(6)+ (S)/(12) =(S)/(4) `
` therefore " " ` Average speed ` =("total distance ")/("total time") =(S)/(S//4) =4m//s`