Question

A train starts from rest with an acceleration of 0.5m/ss.find its speed in km/h when it has moved through 100m

Answer 1

Answer

• Final velocity = 36 km/h

Given

• A train starts from rest with an acceleration of 0.5 m/s²

To Find

• Speed in km/h when it has moved through 100 m

Concept Used

3 rd equation of motion

• v² - u² = 2as

__________________

• 1 km = 1000 m
• 1 h = 3600 s

Solution

Initial velocity , u = 0 m/s [ ∵ starts from rest ]

Acceleration , a = 0.5 m/s²

Final velocity , v = ? m/s

Distance , s = 100 m

Apply 3 rd equation of motion .

⇒ v² - u² = 2as

⇒ v² - 0² = 2(0.5)(100)

⇒ v² = 100

⇒ v = 10 m/s

So , Final velocity = 10 m/s

We need to convert it into km/h . So ,

$\rm v=10\ m/s\\\\\implies \rm v=10 \times \dfrac{3600}{3600}\ m/s\\\\\implies \rm v=\dfrac{1000}{3600} \times 36\ m/s\\\\\implies \rm v=\dfrac{1000\ m}{3600\ s}\times 36\\\\\implies \rm v=\dfrac{1\ km}{1\ h}\times 36\\\\\implies \rm v=36\ km/h$

Answer 2

Final velocity of train is 36km/hr.

Given :-

• Initial velocity (u) = 0m/s
• Acceleration (a) = 0.5m/s²
• Displacement (s) = 100m

To Find :-

• Final velocity (v) = ?

Solution :-

Applying 3rd equation of motion,

.°. v² = u² + 2as

[ Put the values ]

=> v² = 0² + 2 (0.5)×(100)

=> v² = 100

=> v = √100

=> v = 10m/s .

Hence, the final velocity is 10m/s.

Now, according to question we need to convert it into km/hr .

=> Final velocity = 10 m/s.

=> Final velocity = 10 × 1000/3600 km/hr.

=> Final velocity = 36km/hr.