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A Person is running at a …

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A Person is running at a maximum speed of 4m/s to catch a train.When he is 6 metre away from the door of compartment,the train starts to leave at a constant acceleration of 1m/s .Find the time taken by person to catch train.

  • 1 answers

Naveen Sharma 7 years ago

Ans. Let Train cover a distance d before man caught it in t time.

So, Distance covered by man S = 6+d m

Initial Speed of man u = 4m/s

As man is running with constant speed, So a = 0

Using

{tex}S = ut +{1\over 2}at^2{/tex}

{tex}=> 6+d = 4t +{1\over 2}\times 0\times t^2{/tex}

{tex}=> 6+d = 4t +0{/tex}

{tex}=> d = 4t -6 {/tex}………(1)

Similarly initial Speed of Train u = 0

acceleration a = 1m/s2

Distance traveled = d

So,

{tex}=> d = 0\times t+{1\over 2}\times 1\times t^2{/tex}

{tex}=> d ={ 1\over 2} t^2{/tex}………(2)

From (1) & (2)

{tex}=> 4t-6 = {1\over 2}t^2{/tex}

{tex}=> 8t-12 = t^2{/tex}

{tex}=>t^2- 8t+12 =0{/tex}

On solving we get,

t = 6s or 2s

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