Question:
A $100\, m$ long train is moving with a uniform velocity of $45\, km/h$. The time taken by the train to cross a bridge of length $1\, km$ is:
A $100\, m$ long train is moving with a uniform velocity of $45\, km/h$. The time taken by the train to cross a bridge of length $1\, km$ is:
Updated On: Jun 20, 2022
- 58 s
- 68 s
- 78 s
- 88 s
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The Correct Option is D
Solution and Explanation
Total distance covered by train is sum of train's length plus length of bridge.
Total time taken by train to cross the bridge
$=\frac{\text { Total distance }}{\text { Velocity }}$
Total distance $=$ Length of train $+$ Length of bridge
$=100+1000=1100\, m$
Velocity of train $=45 \,km / h$
$=\frac{45 \times 5}{18}=12.5\, m / s$
$\therefore t=\frac{1100}{12.5}=88\, s$
Total time taken by train to cross the bridge
$=\frac{\text { Total distance }}{\text { Velocity }}$
Total distance $=$ Length of train $+$ Length of bridge
$=100+1000=1100\, m$
Velocity of train $=45 \,km / h$
$=\frac{45 \times 5}{18}=12.5\, m / s$
$\therefore t=\frac{1100}{12.5}=88\, s$
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration