1.

A particle starts from rest and travels a distance 's' with uniform acceleration, then it travels a distance '2s' with uniform speed and finally it travels a distance '38' with uniform retardation and comes to rest. If whole motion is in a straight line, the ratio of maximum velocity to average velocity is

Answer»

`6//7`
`4//5`
`5//3`
`5//2`

Solution :Here s= area of v-t graph
LET v be MAXIMUM velocity, then
`s=(1)/(2) ut_(1)`
`:. t_1=(2S)/(v)`
Also `2s=vxxt_(2)`
`t_2=(2s)/(v)`
and`3s=(1)/(2)vt_(3)`
`t_(3)=(6s)/(v)`
Then `v_(av)=(6s)/((2s)/(v)+(2s)/(v)+(6s)/(v))=(6sxxv)/(10 s)=(3)/(5)v`
Now `v_(max)=v`
`:. (v_(max))/(v_(av))=(v)/(3//5v)=(5)/(3)`


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