A particle is moving in a straight line. Its retardation is given as a=−loge2 V, here V is the speed of the particle in m/s. Find the time (in s) in which speed of the particle reduces to half.

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answer is 2.

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Detailed Solution

dVdt=−(loge2)V⇒ VV/2dVV=−(loge2) 0tdt⇒[log V]VV/2=−log 2 [t]⇒logV2−log V=−log 21/2 [t]⇒log12=−(12log 2) t⇒−log2=−(12log 2) t⇒t=2s

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