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`        between two stations a train starting from rest first accelerates uniformly then moves with a constant velocity and finally retards to come to rest if the ratio of the time taken is 1:8:1 and the maximum speed attained is 60 km/hr then what is the average speed of the whole journey? `
2 years ago

```							Let it accelerates with say ‘a’ in time ‘x’ then it reaches a velocity ‘v’ and continues motion for time ‘8x’ abd finally then retards with ‘b’ in time ‘x’.v = 0 + ax=> v = ax=> 60 = ax=> a = 60/xAnd,0 = v – bx=> b = 60/xDistance covered in time of acceleration,S1 = 0 + ½ at2=> S1 = ½ ax2 = ½ × 60/x × x2 = 30xDistance covered while moving with constant velocity is,S2 = vt = 60 × 8x = 480xDistance covered in time of retardation,02 = v2 - 2bS3=> S3 = 602/(2 × 60/x)=> S3 = 30xSo, total distance = 30x + 480x + 30x = 540xTotal time = x + 8x + x = 10xSo, average velocity = 540x/10x = 54 km/h
```
2 years ago
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