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Stopping distance under uniform braking

This type of question, asked 4 times: 25 Jul 2022, 1 Feb 2023, 4 Apr 2024, 9 Apr 2024. All 4 questions below, oldest first.

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  1. Question 1

    25 Jul 2022

    21
    A car is moving with speed of 150 km/h150\text{ }km/h and after applying the brake it will move 27 m27\text{ }m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ____\_\_\_\_ m distance.

  2. Question 2

    1 Feb 2023

    115
    For a train engine moving with speed of 20 ms−120{\text{ }ms}^{- 1}, the driver must apply brakes at a distance of 500 m500\text{ }m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed x ms−1\sqrt{x}{\text{ }ms}^{- 1}. The value of xx is___ (Assuming same retardation is produced by brakes)

  3. Question 3

    4 Apr 2024

    112
    A bus moving along a straight highway with speed of 72 km/h72\text{ }km/h is brought to halt within 4 s4\text{ }s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ____ mm.

  4. Question 4

    9 Apr 2024

    97
    Two cars are travelling towards each other at speed of 20 m s−120\text{ }m{\text{ }s}^{- 1} each. When the cars are 300 m300\text{ }m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s−22\text{ }m{\text{ }s}^{- 2}. The distance between them when they come to rest is:

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