Question

a train moving with a velocity 36km/h us brought to rest applying brakes in 5s . calculate the retardation and distance travelled during this period​

Answer 1

Answer:

• Retardation is 2 m/s².

• Distance travelled is 25 m.

Explanation:

To find : Retardation and distance travelled.

Given that,

• Initial velocity, u is 36 km/h.
• Final velocity, v is 0 km/h
• Time , t is 5 s.

We know,

• Acceleration = v - u/t

Conversion :

• 35 km/h = (36 × 5)/18 = 10 m/s

• 0 km/h = 0 m/s.

Now, Put values :

→ Acceleration = 0 - 10/5

→ Acceleration = -2

• Retardation is negative acceleration.

Thus,

Retardation is 2 m/s².

Now,

We also know,

Second equation of motion :

• s = ut + 1/2 at²

[s is distance travelled]

Put all values :

→ s = 10 × 5 + 1/2 × (-2) × (5)²

→ s = 50 + 1/2 × (-2) × 25

→ s = 50 - 50/2

→ s = (100 - 50)/2

→ s = 25

Thus,

Distance travelled is 25 m.

Answer 2

Given :-

a train moving with a velocity 36km/h is brought to rest applying brakes in 5s

To Find :-

Calculate the retardation and distance traveled during this period​

Solution :-

${\large{\bf{\underline{\underline{\dag Part\;I:-}}}}}$

Retardation is defined as negative acceleration. It occurs when initial velocity is greater than final velocity

${\large{\boxed{\sf 1\;km/h=\dfrac{5}{18}\;m/s}}}$

$\sf:\implies 36\;km/h=36\times\dfrac{5}{18}$

$\sf:\implies 36\;km/h=2\times 5$

$\sf:\implies 36\;km/h=10\;m/s$

We know that

${\large{\boxed{\sf v=u+at}}}$

$\sf:\implies 0=10+a(5)$

$\sf:\implies 0-10=5a$

$\sf:\implies -10=5a$

$\sf:\implies \dfrac{10}{-5}=a$

$\sf:\implies -2=a$

${\large{\boxed{\sf Retardation=-(Acceleration)}}}$

$\sf:\implies Retardation=-(-2)$

$\sf:\implies Retardation=2\;m/s^2$

${\large{\bf{\underline{\underline{\dag Part\;II:-}}}}}$

We know that

${\large{\boxed{\sf v^2-u^2=2as}}$

$\sf:\implies (0)^2-(10)^2=2(-2)(s)$

$\sf:\implies 0-100=-4s$

$\sf:\implies -100=-4s$

$\sf:\implies \dfrac{-100}{-4}=s$

$\sf:\implies \dfrac{100}{4}=s$

$\sf:\implies 25=s$

${\textsf{\textbf{\underline{Hence, Retardation is 2 and Distance travelled is 25 m}}}}$