The engine of a motorcycle can produce a maximum acceleration $5 \,ms^{-2}$. Its brakes can produce a maximum retardation $10\, ms^{-2}$. What is the minimum time in which it can cover a distance of $1.5\, km$.........$sec$
$30$
$15$
$10$
$5 $
The engine of a motorcycle can produce a maximum acceleration $5 \,ms^{-2}$. Its brakes can produce a maximum retardation $10\, ms^{-2}$. What is the minimum time in which it can cover a distance of $1.5\, km$.........$sec$
If a body starts from rest with acceleration $\alpha $ and then retards with retardation $\beta $ and comes to rest. The total time taken for this journey is $t $ and distance covered is $S$ then
$S = \frac{1}{2}\frac{{\alpha \beta \,{t^2}}}{{(\alpha + \beta )}} = \frac{1}{2}\frac{{5 \times 10}}{{(5 + 10)}} \times {t^2}$
$⇒$ $1500 = \frac{1}{2}\frac{{5 \times 10}}{{(5 + 10)}} \times {t^2}$ $ \Rightarrow \;\;t = 30\sec $
$S = \frac{1}{2}\frac{{\alpha \beta \,{t^2}}}{{(\alpha + \beta )}} = \frac{1}{2}\frac{{5 \times 10}}{{(5 + 10)}} \times {t^2}$
$⇒$ $1500 = \frac{1}{2}\frac{{5 \times 10}}{{(5 + 10)}} \times {t^2}$ $ \Rightarrow \;\;t = 30\sec $
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