A bus is travelling at 36 km h-1 when the driver sees an obstacle 30 m ahead. Class 9

A bus is travelling at 36 km h^-1 when the driver sees an obstacle 30 m ahead. Class 9

Question 1.

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? Class 9

Answer:

Given:

1. Initial speed of bus, u = 36 km h^-1 = 36/3.6 = 10 m s^-1
2. Reaction time = 0.5 s (during this time, the bus continues at 10 m s^-1)
3. Deceleration after braking, a = -2.5 ms^-2
4. Obstacle is 30 m ahead

Step 1: Distance covered during reaction time (before brakes are applied)

During reaction time, bus moves at 10 m s^-1 for 0.5 s:

d₁ = u × reaction time = 10 × 0.5 = 5 m

Step 2: Distance covered after brakes are applied until the bus stops

After braking: u = 10 m s^-1, v = 0, a = -2.5 m s^-2

Using v² = u² + 2as:

0 = 10² + 2 × (-2.5) × s

0 = 100 - 5s

5s = 100

s = 20 m

d₂ = 20 m

Step 3: Total distance covered before stopping

Total stopping distance = d₁ + d₂ = 5 + 20 = 25 m

Conclusion: The total distance covered by the bus from when the driver sees the obstacle to when the bus completely stops is 25 m. Since the obstacle is 30 m away and the bus stops after only 25 m, yes, the bus will be able to stop before reaching the obstacle. The bus stops 30 - 25 = 5 m before the obstacle.