A car of mass 800 kg traveling at 54 km h⁻¹ is brought to rest in 60 meters. Find the average retarding force on the car. What has happened to the original K.E? (Ans: 1500 N)



Given:

Mass of car = m = 800 kg

Initial velocity of the car = `\vec {v_i}` = 54 km h⁻¹  = 15 m s⁻¹

Distance traveled =  d =  60 m 

Final velocity of the car = `\vec {v_f}` = 0 m s⁻¹

To Find:

Average force =  F = ?   


Solution:


According to work energy principal

Work done = change in K.E.

Fｘd = `\frac {1}{2}` m `\v_f²` - `\frac {1}{2}` m `\v_i²`

Fｘd = `\frac {1}{2}` m ( `\v_f²` - `\v_i²`)


by putting the corresponding values

Fｘ60 m =  `\frac {1}{2} 800 kg` ( (0 m s⁻¹)² - (15 m s⁻¹)²)

Fｘ60 m =  400 kg ( 0 m s⁻¹ - 225 m² s⁻²)

F = `\frac {-90000 kg m² s⁻²}{60 m}`


F = -1500 N -------------Ans.

the negative sign shows that the force is retarding force.



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