Question

An object moving with a speed of 6.25m/s , is decelereted at a rate given by dv/dt = -2.5√v ,where v is instantaneous speed . the time taken by the object to come to rest would be [AIEEE 2011]
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Answer 1

Explanation :- Given dv/dt = -2.5√v

let it comes to rest at time 't'

since ,

• =>dv/√v = -2.5dt
• => dv/√v = -2.5dt
• =>₆•₂₅∫⁰ v-½dv = -2.5 ₀∫ ᵗ dt
• => -2.5 [t] ᵗ₀=[2v½]₀⁶•²⁵
• => t = 2s Answer

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