An object is subjected to retardation,dv/dt =-5√v,which has initial velocity of 4 m/s.The time taken by the object to come to rest would be___.The ans is 4/5 s.explain how?
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= -12 / -10v^3'2 = t
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Answer:
4/5 seconds.
Explanation:
Since we know that the initial velocity is 4 m/s and the final velocity must be 0 m/s so that the body comes to rest. hence the limit for the integration will be from 4 m/s to 0 m/s.
So, dv/dt = -5√v
Hence, to get the value of time we need to integrate.
√vdv integration from 4 to 0 = -5dt from 0 to t.
On solving the above integration we will get [2√v] from 4 to 0 = -5t so we will get the value of the time t to be = -4/5 seconds.
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