Question

A train is moving with a velocity of 108 km/h and it take 4s to stop after the brakes are applied. Calculate the force exerted by the brakes on the train if its mass is 10000 kg.​

Answer 1

$\huge\tt{Answer:-}$

$\bf{Given:-}$

• Initial Velocity $(u)$ = $108 \ km \ {h}^{-1}$.
• Final Velocity $(v)$ = $0 \ km \ {h}^{-1}$.
• Time Taken $(t)$ = $4 \ s$.
• Mass of the train $(m)$ = $10,000 \ kg$.

$\bf{To \ Find:-}$

Force exerted by the brakes to the train to stop it.

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Finding Acceleration (Retardation) of the Train:-

(Refer to the Attachment)

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Now, Finding Force $(F)$ exerted:-

We know,

$F = ma$

where,

• F = Force
• m = Mass of the object.
• a = Acceleration.

$\therefore F = 10,000 \ kg \cdot (-7.5 \ m \ {s}^{-2}$

$\implies F = - 75,000 \ kg \ m \ {s}^{-2}$

$\implies F = - 75,000 N$ $...(Ans.)$

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Note:

As per the Newton's third law of motion: "Every action has an opposite reaction which act on the two particles.", we can tell that the train also applied the same force to the brakes.

Thus,

75,000 N + (- 75,000 N)

= 75,000 N - 75,000 N

= 0 N