Question

A train with a mass of 2000 kg coasts on a frictionless track with a speed of 50m/s. How large a constant retarding
force is required to stop it in a distance of 100 m?
57000N
37000N
9000ON
63000N
25000N​

Answer 1

Given :

• Mass of a train = 2000 kg

• Initial velocity of the train = 50 m/s

• Final velocity of the train = 0 m/s

• Distance = 100 m

To find :

• Retarding force

Solution :

• Firstly, we shall find the acceleration of the train by using the third equation of motion and then by using the formula to calculate force we will get our required answer.

Third equation of motion :-

• v² - u² = 2as

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• s = distance/displacement

we have,

• v = 0 m/s

• u = 50 m/s

• a = ?

• s = 100 m

Substituting the values :-

→ (0)² - (50)² = 2(a)(100)

→ - 50² = 200 × a

→ - 2500 ÷ 200 = a

→ - 25 ÷ 2 = a

→ - 12.5 = a

Therefore, acceleration of the train = - 12.5 m/s²

Negative acceleration is known as retardation.

So, retardation = 12.5 m/s²

Retarding force = Mass × Retardation

Substituting the given values :-

→ Retarding force = 2000 × 12.5

→ Retarding force = 25000 N

★ Therefore, retarding force = 25000 N