The velocity time graph of a particle moving along a straight line is shown in the figure. In the time interval from `t=0` to `t=8` second, answer the following three question.

The value of `("magnitude of maximum velocity")/("magnitude of average velocity")` for the given time interval is :

Options

A. `(8)/(9)`
B. `(8)/(3)`
C. `(16)/(9)`
D. `(16)/(3)`

Answer

D

Explanation

Distance travelled
`=(1)/(2)xx4 xx(2+4)(1)/(2)-xx 2 xx(2+4)=6m`
magnitude of displacement
`=(1)/(2)xx 4xx(2+4)(1)/(2)-xx 2xx(2+4)=6m`
average speed `= (18)/(8)`
`|"average velocity"| = (6)/(8)`
`("maximum speed")/("average speed")=(4)/(18)xx8=(16)/(9)`
And `(|"maximum velocity"|)/(|"average velocity"|)=(4)/(6) xx8 =(16)/(3)`.