Question

A train starting from a railway station and moving with uniform acceleration attains a speed 40 km h−1 in 10 minutes. Find its acceleration.

0.172 m/s²

0.185 m/s²

0.956 m/s²

None of these



please answer this​

Answer 1

EXPLANATION.

Train starting from a railway station.

Moving with uniform acceleration of speed = 40 km/hr.

Time = 10 minutes.

As we know that,

Let the initial speed of train = u = 0.

Final velocity = v = 40 km/hr.

⇒ 40 x 5/18 = 100/9 m/s.

Time = 10 minutes.

⇒ 10 x 60 = 600 seconds.

As we know that,

Newton's first equation.

⇒ v = u + at.

Using this formula in the equation, we get.

⇒ 100/9 = 0 + (a)600.

⇒ 100/9 = 600a.

⇒ 1/9 = 6a.

⇒ 1 = (6a)(9).

⇒ 1 = 54a.

⇒ a = 0.0185 m/s².

Answer 2

$\large\underline{\sf{Given}}$

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» Final velocity (v) of train = 40 km/h.

» Final velocity (v) in m/s = 40 × 5/18 = 100/9 m/s.

» Time taken (t) = 10 mins.

» Time taken (t) in seconds = 10 × 60 = 600 s.

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$\large\underline{\sf{To\:Find}}$

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» Acceleration (a) of train?

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$\large\underline{\sf{Solution}}$

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$\underbrace{\underline{\sf{\bigstar\:Understanding\:the\:Question\:::}}}$

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Here, we are given that a train starting from a railway station and moving with uniform acceleration attains a speed 40 km/h (100/9 m/s) in 10 minutes. Hence, we have final velocity and time taken. We are not given initial velocity. So, let initial velocity (u) = 0 m/s. Now, we can easily find acceleration of train by using first equation of motion i.e, v = u + at. Where, 'v' is final velocity, 'u' is initial velocity, 't' is time taken and 'a' is acceleration. So, let's solve it!

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$\sf \longrightarrow\: v = u + at$

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Putting all known values,

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$\sf \longrightarrow\: \dfrac{100}{9} = 0 + a\big(600\big)$

$\\ \sf \longrightarrow\: 600a = \dfrac{100}{9}$

$\\ \sf \longrightarrow\: a = \dfrac{1\cancel{00}}{9\:\times\:6\cancel{00}}$

$\\ \sf \longrightarrow\: a = \dfrac{1}{9\:\times\:6}$

$\\ \sf \longrightarrow\: a = \dfrac{1}{54}$

$\\ \sf \longrightarrow\: \pink{Acceleration\:\big(a\big)\:of\:train = 0.0185\:m/s^2}$

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$\therefore\:{\underline{\textsf{\textbf{Last\:option\:(None\:of\:these)\:\sf{is\:correct!}}}}}$

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$\large\underline{\sf{More\:to\:know}}$

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Three equations of motion,

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• v = u + atㅤㅤㅤㅤ[Used above]

• s = ut + ½ at²

• v² = u² + 2as

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Some important definitions,

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• Acceleration

Acceleration is the process where velocity changes. Since, velocity is the speed and it has some direction. So, change of velocity is considered as acceleration.

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• Initial velocity

Initial velocity is the velocity of the object before the effect of acceleration.

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• Final velocity

After the effect of acceleration, velocity of the object changes, the new velocity gained by the object is known as final velocity.

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