Question

a train starting from a railway station and moving with uniform acceleration attains a speed of 40 km/h in 5 mins. find its acceleration​

Answer 1

Given

• A train starts from a railway station and moves with uniform acceleration.
• It attains a speed of 40 km/h in 5 minutes.

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To Find

• It's acceleration

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Solution

Since the train starts from rest, its initial velocity would be 0 m/s.

Final Velocity → 40 km/h

We will convert it in m/s.

$\implies 40 \times \dfrac{5}{18}$

$\implies \dfrac{200}{18}$

$\implies \dfrac{100}{9}$ m/s

∴ Final Velocity = 100/9 m/s

Time Taken → 5 mins

We will convert it into seconds.

⇒ 5 × 60

⇒ 300 sec

∴ Time = 300 sec

Since acceleration is the rate of change of velocity, we have found the initial velocity, final velocity, and time taken which is required for finding the acceleration.

We will apply the 1st equation of motion.

First equation of Motion → v = u+at

Here,

v ⇒ Final Velocity = 100/9 m/s

u ⇒ Initial Velocity = 0 m/s

t ⇒ Time Taken = 300 sec

a ⇒ Acceleration = a m/s²

$\implies \dfrac{100}{9}= 0+a(300)$

$\implies \dfrac{100}{9} = 300a$

$\implies 300a = \dfrac{100}{9}$

$\implies a = \dfrac{100}{9} \div 300$

$\implies a = \dfrac{100}{9} \times \dfrac{1}{300}$

$\implies a = \dfrac{1}{9} \times \dfrac{1}{3}$

$\implies a = \dfrac{1}{27}$

$\implies a=0.037 \ m/s^{2}$

∴ Its acceleration is 0.037 m/s²

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