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A bus is travelling at 36 km h⁻¹ when the driver sees an obstacle 30 m ahead. The driver takes 0.5 seconds to react before pressing the brake. Once the brake is applied, the velocity of the bus reduces with constant acceleration of 2.5 m s⁻². Will the bus be able to stop before reaching the obstacle?
Show Answer
\(u = 36\ \text{km h}^{-1} = 10\ \text{m s}^{-1}\).
Reaction distance (before braking) \(= 10 \times 0.5 = 5\ \text{m}\).
Braking distance: \(v^2 = u^2 + 2as \Rightarrow 0 = 10^2 + 2(-2.5)s \Rightarrow s = \dfrac{100}{5} = 20\ \text{m}\).
Total stopping distance \(= 5 + 20 = 25\ \text{m} < 30\ \text{m}\). Yes, the bus stops in time , with 5 m to spare.
