Calculate the total distance covered by a train before coming to rest if its initial speed is 30ms-1 with a constant retardation of 0.1m-2

Answer Details

To solve this problem, we can use the following kinematic equation:
v^2 = u^2 + 2as
where:
- v is the final velocity (which is zero since the train comes to rest)
- u is the initial velocity (which is 30 m/s)
- a is the acceleration (which is the negative of the retardation, -0.1 m/s^2)
- s is the distance covered
Substituting the values into the equation, we get:
0^2 = (30 m/s)^2 + 2(-0.1 m/s^2)s
Simplifying, we get:
0 = 900 - 0.2s
0.2s = 900
s = 4500 meters
Therefore, the total distance covered by the train before coming to rest is 4500 meters.
Explanation:
When a train is moving with a certain velocity and then comes to rest due to a constant retardation, its total distance covered can be calculated using the above kinematic equation. This equation relates the initial velocity, final velocity, acceleration, and distance covered by the train. By substituting the given values into the equation and solving for the distance covered, we get the answer. In this case, the train starts with an initial velocity of 30 m/s and comes to rest with a constant retardation of 0.1 m/s^2. The total distance covered by the train before coming to rest is found to be 4500 meters.