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Standard XII

Physics

v-t Graph

Two trains on...

Question

Two trains one travelling at $15 m s^{- 1}$ and other at $20 m s^{- 1}$ are headed towards one another a straight track. Both the drivers apply brakes simultaneously when they are $500 m$ apart. If each train has a retardation of $1 m s^{- 2}$ , the separation after they stop is

192.5 m

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225.5 m

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587.5 m

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155.5 m

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Solution

The correct option is C $587.5 m$
To find stopping distance
For first train
$v^{2} - u^{2} = 2 a s$
$0 - 15^{2} = - 2 \times 1 \times s$

$⟹ s = \frac{225}{2} m = 112.5 m$

For second train
$v^{2} - u^{2} = 2 a s$
$0 - 20^{2} = 2 \times (- 1) \times s$
$⟹ 200 m$

$∴$ Separation $= 500 + 200 - 112.5$
$= 300 - 112.5$
$= 587.5 m$

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Two trains one travelling at 15ms−1 and other at 20ms−1 are headed towards one another a straight track. Both the drivers apply brakes simultaneously when they are 500m apart. If each train has a retardation of 1ms−2, the separation after they stop is

The correct option is C 587.5mTo find stopping distance For first train v2−u2=2as0−152=−2×1×s⟹s=2252m=112.5mFor second train v2−u2=2as0−202=2×(−1)×s⟹200m∴ Separation =500+200−112.5=300−112.5=587.5m

Two trains one travelling at $15 m s^{- 1}$ and other at $20 m s^{- 1}$ are headed towards one another a straight track. Both the drivers apply brakes simultaneously when they are $500 m$ apart. If each train has a retardation of $1 m s^{- 2}$ , the separation after they stop is