Physics, asked by sharmadsatyam, 5 hours ago

A train is travelling at a speed of 90km 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​

Answers

Answered by Yuseong
7

Answer:

625 m

Explanation:

As per the provided information in the given question, we have :

  • Initial velocity (u) = 90 km/h
  • Acceleration (a) = -0.5 m/s²
  • Final velocity (v) = 0 (As it comes to rest)

Converting initial velocity in m/s :

\longrightarrow\sf{ u = 90\; kmh^{-1}}

\longrightarrow\sf{ u = \Bigg ( 90 \times \dfrac{5}{18} \Bigg ) \; ms^{-1}}

\longrightarrow\sf{ u = \Bigg ( 5 \times 5\Bigg ) \; ms^{-1}}

\longrightarrow\boxed{\sf{ u = 25 \; ms^{-1}}}

Now, by using the third equation of motion :

\longrightarrow v² - u² = 2as

  • s denotes distance
  • u denotes initial velocity
  • a denotes acceleration
  • v denotes final velocity

\longrightarrow \sf {(0)^2 - (25)^2 = 2 \times (-0.5) \times s} \\

\longrightarrow \sf {0-625 = -1s} \\

\longrightarrow \sf {-625 = -1s} \\

\longrightarrow \sf {\cancel{\dfrac{-625 }{-1}}= s} \\

\longrightarrow \boxed{\sf {625 \; m = s}} \\

Therefore, distance travelled before coming to rest is 625 m.

\rule{200}2

More Information:

First equation of motion :

\longrightarrow v = u + at

Second equation of motion :

\longrightarrow s = ut + ½at²

Third equation of motion :

\longrightarrow v² = u² + 2as

Where,

v denotes final velocity

u denotes initial velocity

a denotes acceleration

s denotes distance

t denotes time

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