The distance- time graph for the motion of three vechicles,A , B and C are as shown in the figure , `S_(A), S_(B) nd S_(C)` are the speeds, of A,B and C , respectively , compare the speeds of A, B and C.

Options

A. `S_(A) gt S_(B) gt S_(C)`
B. `S_(A) lt S_(B) lt S_(C)`
C. `S_(A)=S_(B)=S_(C)`
D. `S_(A) lt S_(B) lt S_(C)`

Answer

A

Explanation

Let `d_(A), d_(B) and d_(C)` be the distances covered by the cars, A,B and C are the cars.
Given that `d_(A)=d_(B)=d_(C)`
Let `t_(A),t_(B) and t_(C)` be the timetaken by car A,B and C.
Then `t_(A) lt t_(B) lt t_(C)`
We know `S_(A)=(d_(A))/(t_(A)), S_(B)=(d_(B))/(t_(B))and S_(C)=(d_(C))/(t_(C))`
`rArr S_(A) gt S_(B) gt S_(C)`.
Hence the correct option is (a).