A train travels for $30$ minutes with a velocity of $54 k m / h$ and then for $120$ minutes with a velocity of $72 k m / h$ in the same direction. Calculate the average velocity of the train.

15 m / s

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16 m / s

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19 m / s

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17 m / s

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Solution

The correct option is C $19 m / s$
Given:
$v_{1}$ = $54 k m / h$ = $15 m / s$
$t_{1}$ = $30 m i n u t e s$ = $1800 s e c$
$v_{2}$ = $72 k m / h$ = $20 m / s$
$t_{2}$ = $120 m i n u t e s$ = $7200 s e c$
Displacement travelled in the $t_{1}$
=> $s_{1}$ = $v_{1}$ $t_{1}$ = $27000 m$
Displacement travelled in the $t_{2}$
=> $s_{2}$ = $v_{2}$ $t_{2}$ = $144000 m$
Thus, Avg. velocity = $\frac{T o t a l d i s t a n c e c o v e r e d}{T o t a l t i m e}$

=> $\frac{27000 m + 144000 m}{1800 s e c + 7200 s e c}$ => $19 m / s$

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A train travels for 30 minutes with a velocity of 54 km/h and then for 120 minutes with a velocity of 72 km/h in the same direction. Calculate the average velocity of the train.

A train travels for $30$ minutes with a velocity of $54 k m / h$ and then for $120$ minutes with a velocity of $72 k m / h$ in the same direction. Calculate the average velocity of the train.