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 \(\alpha\) 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 \(s = \frac{1}{2} \frac{\alpha \beta t^{2}}{(\alpha + \beta)} = \frac{1}{2} \frac{5 \times 10}{(5 + 10)} \times t^{2}\)
⇒ ⇒ \(1500 = \frac{1}{2} \times \frac{5 \times 10}{(5 + 10)} \times t^{2}\) \(\Rightarrow t = 30 \text{ sec}\) .
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