A train is moving witha a velocity of 30m/s when brakes are applieded, it is found that the velocity reduces 10m/s in 240m. When the velocity of the train becomes zero, the total distance travelled is what

Initial velocity, u = 30 m/s
Velocity after some distance, v = 10 m/s
Distance covered, s = 240 m

Step 1: Find Acceleration
Using the equation of motion:

v² = u² + 2as

Substituting the given values:

(10)² = (30)² + 2a(240)
100 = 900 + 480a
100 - 900 = 480a
-800 = 480a
a = -800 / 480
a = -5/3 m/s²

The acceleration is negative because the train is decelerating.

Step 2: Find Total Distance Traveled
Now, we calculate the total distance traveled until the train stops. We use the same equation:

v² = u² + 2as

Here, the new initial velocity is u = 10 m/s, and the final velocity is v = 0.

0 = (10)² + 2(-5/3)s
0 = 100 - (10/3)s
(10/3)s = 100
s = (100 × 3) / 10
s = 30 m

Step 3: Calculate Total Distance
The total distance traveled is:

240 m + 30 m = 270 m

Thus, the total distance traveled by the train before stopping is 270 meters.