Between the two stations, a train accelerates uniformly at first, then moves with constant velocity and finally retards uniformly. If the ratio of the time taken is $1 : 8 : 1$ and the maximum speed attained be $60 k m / h$ , then what is the average speed over the whole journey -

52 k m / h

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48 k m / h

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54 k m / h

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56 k m / h

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Solution

The correct option is C $54 k m / h$
We have $60 = v = u + a t_{1} = a t_{1}$
$\Rightarrow a = \frac{60}{t_{1}}$
Also, $s_{1} = u t_{1} + \frac{1}{2} a t_{1}^{2} = \frac{1}{2} \frac{60}{t_{1}} t_{1}^{2} = 30 t_{1}$
Now, $v^{2} = u^{2} + 2 a s_{1}$
From, $s_{1} = \frac{1}{2} a t_{1}^{2}$ we substitute $a = \frac{2 s_{1}}{t_{1}^{2}}$ $\Rightarrow$ $v = \frac{2 s_{1}}{t_{1}}$
The $s_{2}$ distance is traveled at this velocity. Thus we get:
$s_{2} = v t_{2} = \frac{2 s_{1}}{t_{1}} t_{2}$
But the ratio of times is given as $\frac{t_{2}}{t_{1}} = \frac{8}{1}$ or $t_{2} = 8 t_{1}$ $\Rightarrow$ $s_{2} = 16 s_{1}$
And we got $s_{1} = 30 t_{1}$ $\Rightarrow$ $s_{2} = 480 t_{1}$
Given: $s_{3} = s_{1} = 30 t_{1}$
Thus, we get the average speed as:
$\frac{d i s t a n c e t r a v e l l e d}{t i m e t a k e n} = \frac{30 t_{1} + 480 t_{1} + 30 t_{1}}{t_{1} + 8 t_{1} + t_{1}} = 54 k m / h r$

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Similar questions

Q. Between the two stations, a train uniformly accelerates from rest at first, then moves with constant velocity and finally decelerates uniformly to come to rest. If the ratio of the time taken is

1 : 8 : 1

and the maximum speed attained is

60 km/h

, then what is the average speed over the whole journey?

Between two stations, a train accelerates from rest uniformly at first, then moves with constant velocity, and finally retards uniformly to come to rest. If the ratio of the time taken is 1:8:1 and the maximum speed attained be 60km/hr, then what is the average speed over the whole journey?

a) 48km/h

b) 52km/h

c) 54km/h

d) 56Km/h

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Between the two stations, a train accelerates uniformly at first, then moves with constant velocity and finally retards uniformly. If the ratio of the time taken is 1:8:1 and the maximum speed attained be 60 km/h, then what is the average speed over the whole journey -

Between the two stations, a train accelerates uniformly at first, then moves with constant velocity and finally retards uniformly. If the ratio of the time taken is $1 : 8 : 1$ and the maximum speed attained be $60 k m / h$ , then what is the average speed over the whole journey -