Question

a train accelerates unifomly from 36km/h to 72 km/h in 20 s. find the distance travelled by it.​

Answer 1

Required Answer :

The distance travelled by the train = 300 m

Given :

• Initial velocity of the train = 36 km/h
• Final velocity of the train = 72 km/h
• Time = 20 seconds

To find :

• Distance travelled by it

Solution :

Firstly, we will change the units of the velocity from km/h into m/s then by using the first equation of motion, we will calculate the acceleration of the train and then by using the third equation of motion we will calculate the distance travelled by the train.

To convert the value of initial and final velocity from km/h into m/s, multiply it by 5/18.

→ Initial velocity = 36 × 5/18

→ Initial velocity = 2 × 5

→ Initial velocity = 10 m/s

→ Final velocity = 72 × 5/18

→ Final velocity = 4 × 5

→ Final velocity = 20 m/s

Calculating the acceleration :-

First equation of motion :-

• v = u + at

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

we have,

• v = 20m/s
• u = 10 m/s
• t = 20 s

Substituting the given values :-

⠀⠀⠀⇒ 20 = 10 + (a)(20)

⠀⠀⠀⇒ 20 = 10 + 20a

⠀⠀⠀⇒ 20 - 10 = 20a

⠀⠀⠀⇒ 10 = 20a

⠀⠀⠀⇒ 10/20 = a

⠀⠀⠀⇒ 1/2 = a

⠀⠀⠀⇒ 0.5 = a

Acceleration of the train = 0.5 m/s²

Now, calculating the distance travelled by the train :-

Third equation of motion :-

• v² - u² = 2as

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• s = Distance

we have,

• v = 20m/s
• u = 10 m/s
• a = 0.5 m/s²

Substituting the given values :-

⠀⠀⠀⇒ (20)² - (10)² = 2(0.5)(s)

⠀⠀⠀⇒ 400 - 100 = 1 × s

⠀⠀⠀⇒ 300 = s

Therefore, the distance travelled by the train = 300 m