Question

A train is travelling at a speed of 90 km h-1 brakes are applied so as to produce a uniform acceleration of -0.5ms-².find how far the train will go before it is brought to rest.​

Answer 1

Concept:-

we are provided with a train traveling at a speed of 90km/hr i.e 25 m/s. Brakes are applied to it in order to bring it to rest (final velocity of 0 m/s).

The application of brakes produces retardation (negative acceleration) of -0.5 m/s². We are asked to find the distance traveled by it after the application of brakes.

Solution:-

By using 3rd Kinematical equation:-

$\quad\leadsto\quad\underline{\boxed{\sf v^{2} - u^{2}= 2as }}\bigstar$

where, v, u, a, and s represent final velocity, initial velocity, acceleration, and distance respectively.

substitute the given values in the equation:-

$\\\quad\longrightarrow\quad\tt v^{2} = u^{2} -2as$

$\\\quad\longrightarrow\quad\tt (0)^{2} - (25)^{2} =2(-0.5)s$

$\\\quad\longrightarrow\quad\tt (0) - 625 = -S$

$\\\quad\therefore\quad \boxed{\bf S = 625 \:m}\bigstar$

hence, the required answer is 625 m

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