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The minimum work done required to accele...

The minimum work done required to accelerate a truck on a horizontal road from rest to speed `v`

A

`.

B

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C

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D

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Text Solution

Verified by Experts

The correct Answer is:
A
Minimum work done to accelerate the truck from speed 0 to `v` and from `v` to `2v` are
`DeltaW_(1)=(1)/(2)mv^(2)-(1)/(2)m(0)^(2)=(1)/(2)mv^(2)`
and `DeltaW_(2)=(1)/(2)m(2v)^(2)-(1)/(2)m(v)^(2)=(3)/(2)mv^(2)`
`:. DeltaW_(1) lt DeltaW_(2)`
Sol. For `W` to be maximum `,(dW)/(dx)=0,`
`i.e. F(x) =0rArr x=l,x=0`
Clearly for `d=l`, the work done is maximum.
Alternate Solution `:`
External force and displacement are in the same direction
`:. ` Work will be positive continuously so it will be maximum when displacement is maximum.
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