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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 km h -1 = 10 m s -1 .
Reaction distance (before braking) = 10 × 0.5 = 5 m .
Braking distance: v 2 = u 2 + 2as ⇒ 0 = 10 2 + 2(-2.5)s ⇒ s = 100 5 = 20 m .
Total stopping distance = 5 + 20 = 25 m < 30 m . Yes, the bus stops in time , with 5 m to spare.
| Distance | Value |
|---|---|
| Reaction (0.5 s) | 5 m |
| Braking | 20 m |
| Total stopping | 25 m |
| Obstacle ahead | 30 m |
| Stops in time? | Yes — 5 m to spare |
