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A train 471 m long is moving on a straight track with a speed of 75.1 km/h. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 15 km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing. Answer in units of s.

Respuesta :

Answer:

[tex]t = 37.6 s[/tex]

Explanation:

As we know that train is initially moving with the speed

[tex]v_i = 75.1 km/h[/tex]

now we know that

[tex]v_i = 20.86 m/s[/tex]

now the final speed of the train when it crossed the crossing

[tex]v_f = 15 km/h[/tex]

[tex]v_f = 4.17 m/s[/tex]

now we can use kinematics here

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

[tex]4.17^2 - 20.86^2 = 2 a(471)[/tex]

[tex]a = -0.44 m/s^2[/tex]

Now the time to cross that junction is given as

[tex]v_f - v_i = at[/tex]

[tex]4.17 - 20.86 = a(-0.44)[/tex]

[tex]t = 37.6 s[/tex]

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