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The driver of a train moving at 20m/s sights another train moving at 4m/s on the same track and in the same direction. He immediately applies brake and the train begins to retard at 1m/s2 . What should be the distance between the two trains at the instant of first sight if collision is to be avoided?
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The driver of a train moving at 20m/s sights another train moving at 4...
Problem Statement

The driver of a train moving at 20m/s sights another train moving at 4m/s on the same track and in the same direction. He immediately applies brake and the train begins to retard at 1m/s2. What should be the distance between the two trains at the instant of first sight if collision is to be avoided?

Solution

To solve this problem, we need to use the formula for distance travelled by a body under uniform acceleration:

s = ut + 1/2 at^2

where s is the distance travelled, u is the initial velocity, a is the acceleration, and t is the time taken.

We can break down the problem into the following steps:

Step 1: Find the relative velocity between the two trains

The relative velocity between the two trains is given by:

v_rel = v1 - v2

where v1 is the velocity of the first train and v2 is the velocity of the second train.

v_rel = 20 - 4 = 16m/s

Step 2: Find the time taken for the first train to come to a stop

The first train is slowing down at a rate of 1m/s^2. We can use the formula:

v = u + at

where v is the final velocity (0m/s), u is the initial velocity (20m/s), a is the acceleration (-1m/s^2), and t is the time taken.

0 = 20 - t

t = 20s

Step 3: Find the distance travelled by the first train during this time

We can use the formula:

s = ut + 1/2 at^2

s = 20 x 20 + 1/2 x (-1) x 20^2

s = 200m

Step 4: Find the distance between the two trains at the instant of first sight

The distance between the two trains at the instant of first sight is given by:

d = v_rel x t + 1/2 x (-1) x t^2

d = 16 x 20 + 1/2 x (-1) x 20^2

d = 320m

Therefore, the distance between the two trains at the instant of first sight should be at least 320m if collision is to be avoided.
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The driver of a train moving at 20m/s sights another train moving at 4m/s on the same track and in the same direction. He immediately applies brake and the train begins to retard at 1m/s2 . What should be the distance between the two trains at the instant of first sight if collision is to be avoided?
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