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Standard XII

Physics

Relative Velocity

The driver of...

Question

The driver of a train $A$ running at $25 m s^{- 1}$ sights a train $B$ on the same track with $15 m s^{- 1}$ . The driver of train $A$ applies brakes to produce a deceleration of $1.0 m s^{- 2}$ . If the trains are $200 m$ apart, will the trains collide?

yes

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collision just avoided

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none of these

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Solution

The correct option is C collision just avoided
First we need to find the time taken for A to reach B
Now, $u_{A B} = 25 - 15 = 10 m / s$
Put final velocity $= 0$
$v_{A B} = u_{A B} + a_{A B} t = 0$
$t = 10 s$
Now distance traveled by A in 10s
$s = u t + \frac{1}{2} a t^{2} \Rightarrow s = (25 \times 10) - 50 = 200 m$
Thus collision just avoided.

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The driver of a train A running at 25ms−1 sights a train B on the same track with 15ms−1. The driver of train A applies brakes to produce a deceleration of 1.0ms−2. If the trains are 200m apart, will the trains collide?

The correct option is C collision just avoidedFirst we need to find the time taken for A to reach BNow, uAB=25−15=10m/sPut final velocity=0vAB=uAB+aABt=0t=10sNow distance traveled by A in 10ss=ut+12at2⇒s=(25×10)−50=200mThus collision just avoided.

The driver of a train $A$ running at $25 m s^{- 1}$ sights a train $B$ on the same track with $15 m s^{- 1}$ . The driver of train $A$ applies brakes to produce a deceleration of $1.0 m s^{- 2}$ . If the trains are $200 m$ apart, will the trains collide?