Question

On a

120 km

track, a train travels the just

30 km

at a uniform speed of

30 \frac{km}{h}

. Calculate the speed with which the train should move rest of the track so as to get average speed of

60 \frac{km}{h}

for the entire trip.

Accepted Answer

Given,

The distance of track, $d = 120 km$

Distance travelled by train, $d_{1} = 30 km$

Uniform speed of train, $v = 30 \frac{km}{h}$

Average speed of the train, $V_{a v} = 60 \frac{km}{h}$

Let the rest of the distance of track,

$x = d - d_{1}$ $= 120 - 30$ $= 90 km$

Therefore, time taken by the train to travel distance $d_{1}$

$t_{d_{1}} = \frac{v}{d_{1}}$

$\Rightarrow t_{d_{1}} = \frac{30}{30}$

$\Rightarrow t_{d_{1}} = 1 h . . . . . . . . . . . . . (1)$

Let $v_{1} km h^{- 1}$ is the velocity of rest distance $(x)$ . So, time taken to travelled $x$

$t_{x} = \frac{x}{v_{1}}$

$\Rightarrow t_{x} = \frac{90}{v_{1}} . . . . . . . . . . . . . . . . . . . . . (2)$

Now, the average speed is formulated as, $V_{a v} = \frac{d}{t_{d_{1}} + t_{x}}$

$\Rightarrow 60 = \frac{120}{1 + \frac{90}{v_{1}}} . . . . . . . . . . . . . . . . . From equation (1) and (2)$

$\Rightarrow 1 + \frac{90}{v_{1}} = \frac{120}{60}$

$\Rightarrow 1 + \frac{90}{v_{1}} = 2$

$\Rightarrow \frac{90}{v_{1}} = 2 - 1$

$\Rightarrow v_{1} = 90 km h^{- 1}$

The train should be moved with $90 km h^{- 1}$ rest of the track.

Priyanka B Solutions for Chapter: Motion, Exercise 3: Practice Problems

Priyanka B Physics Solutions for Exercise - Priyanka B Solutions for Chapter: Motion, Exercise 3: Practice Problems

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