The engine of a motorcycle can produce a maximum acceleration 5 m / s 2 . Its brakes can produce a maximum retardation 10 m / s 2 . What is the minimum time in which it can cover a distance of 1.5 km
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If a body starts from rest with acceleration \ddot{f} and then retards with retardation j j' and comes to rest. The total time taken for this journey is t and distance covered is S then \(s = \frac{1}{2} a t^{2} = \frac{1}{2} \frac{5 \times 10}{5 + 10} \times t^{2}\)
⇒ ⇒ \(1500 = \frac{1 \quad 5/10}{2(5+10)} x^{2}\) \(\rightarrow t \quad 30 \quad \mathrm{sec}\) .
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