Question

A metro train runs from station A to B to C. It takes $4$ min travelling from station A to station B. The train halts at station B for $20s.$ Then it starts from station B and reaches station C in next $3$ minutes. At the start, the train accelerates for $10$ sec to reach the constant speed of $72km/hr.$ The train moving at the constant speed is brought to rest in $10$ sec. at next station. (i) Plot the velocity-time graph for the train travelling from the station A to B to C. (ii) Calculate the distance between the stations A, B and C.

Answer 1

$AB=4.6km$
$BC=3.4km$
$AC=8km$
Train takes $10$ sec to reach $72km/h$
$72\frac{km}{h}=22\times \frac{5}{10}=20m/s$
time travel with constant speed
$4\times 60-10-10=220sec$
$Q=\frac{20}{10}=2m/s^2$
distance from A to B
$=\frac{{20}^2}{2\times 2}+20\times 220+\frac{{20}^2}{2\times 2}$
$=100+4400+100$
$=4600m=4.6km$
Distance from B to C
$\frac{{20}^2}{2\times 2}+20\times 160+\frac{{20}^2}{2\times 2}$
$=100+320+100$
$=3400m=3.4km$
Distance from A to C
$A-B=3.4km$
$B-C=4.6km$
$A-C=8km$