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Question
Calculate the work done by the brakes of a car of mass 1000 kg when its speed is reduced from 20 m/s to 10 m/s?
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Solution
Mass of the car, (m) = 1000 kg
Initial velocity, (v1) = 20 m/s
Final velocity, (v2) = 10 m/s
So, initial kinetic energy can be calculated as,
`K.E = 1/2 mv^2`
Therefore ,
`(K.E)_1 = 1/2 (1000)(20)^2` J
= 200000 J
Similarly, final kinetic energy ,
`(K.E)_2 = 1/2 (1000)(10)^2` J
= 50000 J
So,
Work done by the brakes = Change in kinetic energy
Therefore work done by the brakes,
Work done by the brakes
= (K.E)2 – (K.E)1
= (50000 – 200000) J
= –150000 J
= -150 KJ
Negative sign shows the force applied by brakes is opposite to the direction of motion of the body.
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