Question

1)A train is running at a Constant speed of 54 km/hr. What's the speed in m/s? $?$ 2)A train Starting from a railway station attains a Velocity of 30 m/s in a minute, What's the Acceleration?

Answer 1

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$\red{\underline{{ \bf Question \: 1}}}$

• A train is running at a Constant speed of 54 km/hr. What's the speed in m/s?

$\red{\underline{{ \bf Answer }}}$

$\underline {\underline{{\purple{ \sf Given }}}}$

• Speed of train in km/hr ➠ 54 km/hr

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

• Speed of Train in m/s

$\red{ \sf 1 \: km = 1000 \: m}$

$\red{ \sf 1 \: hour = 3600 \: s}$

$\underline {\underline{{ \green{\sf Converting \: it }}}}$

☞ $\blue{ \sf \dfrac{54 \times 36 \cancel{00}}{1\cancel{00}}}$

☞ $\blue{\sf \dfrac{54 \times 10}{36}}$

☞ $\blue{\sf \dfrac{9 \times 10}{6}}$

☞ $\blue{\sf \dfrac{90}{6}}$

☞ $\blue{\sf 15 }$

Therefore, Speed of Train from km/hr ➠ m/s is 15 m/s

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$\red{\underline{{ \bf Question \: 2}}}$

• A train Starting from a railway station attains a Velocity of 30 m/s in a minute, What's the Acceleration?

$\red{\underline{{ \bf Answer }}}$

$\underline {\underline{{\purple{ \sf Given }}}}$

• Initial Velocity (u) ➠ 0 m/s
• Final Velocity (v) ➠ 30 m/s
• Time (t) ➠ 1 min ➠ 60 s

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

• Acceleration of the Train

$\underline {\underline{{ \green{\sf Calculating \: Acceleration }}}}$

Formula Used :- Formula Used :- $\underline{\underline{\boxed{ \pink{\sf v = u + at }}}}$

Substituting Values

☞ $\blue {\sf 30 = 0 + a \times 60}$

☞ $\blue {\sf 30 - 0 = 60a}$

☞ $\blue {\sf 30 = 60a}$

☞ $\blue {\sf 60a= 30}$

☞ $\blue {\sf a = \cancel{\dfrac{30}{60}}}$

☞ $\blue {\sf a = 0.5}$

Therefore, Acceleration of Train is 9.5 m/s²

$\underline {\underline{{\purple{ \sf Additional \: Information }}}}$

• Rate of Change of Velocity with respect to time is known as acceleration and is denoted by 'a'
• Negative acceleration is known as Retardation
• The Speed which a body gains at it's start is known as Initial Velocity and is denoted by 'u'
• The Speed which a body gains after it starts moving is known as Fianal Velocity and is denoted by 'v'

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Answer 2

Question 1)

• A train is running at a Constant speed of 54 km/hr. What's the speed in m/s?

Solution :

• Constant speed of train = 54km/hr.

As we know that,

• 1km = 1000m
• 1m = 1/1000 km

And,

• 1min = 60s
• 1hr = 60 × 60s = 3600s

Converting 54km/hr into m/s

⟶ 54km/hr into m/s

⟶ 54 × 1000/3600

⟶ 54000/3600

⟶ 540/36

⟶ 15m/s

$\underline{ \boxed{ \bf \: 54km/hr = 15m/s}}$

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Question 2)

• A train Starting from a railway station attains a Velocity of 30 m/s in a minute, What's the Acceleration?

Given :

• final velocity (v) = 30m/s
• initial velocity (u) = 0 [train stars from rest ]
• Time = 1min
• Acceleration (a) = ?

Converting 1min to second

• 1min = 60s

So,

• Time = 60s

By using 1st equation of motion

• v = u + at

⟶ 30 = 0 + a × 60

⟶ 30 = 0 + 60a

⟶ 30 = 60a

⟶ 30/60 = a

⟶ a = 0.5m/s

$\underline{ \boxed{ \bf \: Acceleration = 0.5m/s}}$

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