Question

A train moving at a speed of 40 m/s brought to rest by applying a brake in 5s. Calculate the retardation of the train. If the mass of the train is 6000 kg, how much is the retarding force to be applied to stop the train?

Answer 1

Answer

• Retardation will be 8 m/s²
• Force applied will be 48000 N

Explanation

Given

• Initial velocity = 40 m/s
• Final velocity = 0 m/s
• Time = 5 sec
• Mass = 6000 kg

To Find

• Retardation of the body
• Force applied

Solution

• We shall use the first equation of motion to find the acceleration (here negative acceleration/retardation) of the body and then with the help of the Newton's second law we shall find the force applied

✭ Retardation of the body

→ v = u+at

→ 0 = 40 + a×5

→ -40 = 5a

→ -40/5 = a

→ Acceleration = -8 m/s²

But here we are asked retardation so we may ignore the negative sign

→ Retardation = 8 m/s²

✭ Force Applied

→ F = ma

→ F = 6000 × 8

→ F = 48000 N

Note : Here they have asked us the regarding force and so we have taken the acceleration without the negative sign

Answer 2

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A train moving at a speed of 40 m/s brought to rest by applying a brake in 5s. Calculate the retardation of the train. If the mass of the train is 6000 kg, how much is the retarding force to be applied to stop the train?

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u = 20m/s ^ 1

v = 0

t = 5s

Retardation, 

a = tu − v

= 520 − 0 m/s

= 4m/s ^ 2