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Matter In Our Surroundings

Question
CBSEENSC9006351

What is the work to be done to increase the velocity of car from 30 km h-1 to 60 km h-1 if the mass of the car is 1500 kg?

Solution

Mass space of space the space car comma space straight m space equals space 1500 space kg

Initial space velocity space of space the space car
straight u space equals space 30 space km space straight h to the power of negative 1 end exponent space equals space fraction numerator 30 space cross times space 1000 space straight m over denominator 3600 space straight s end fraction space equals space 25 over 3 ms to the power of negative 1 end exponent
Final space velocity space of space the space car comma
straight v space equals space 60 space km space straight h to the power of negative 1 end exponent space equals fraction numerator 60 space cross times space 1000 space straight m over denominator 3600 space straight s end fraction space equals 50 over 3 ms to the power of negative 1 end exponent
So, 
W o r k space d o n e space o n space t h e space c a r space equals space I n c r e a s e space i n space straight K. straight E. space o f space t h e space c a r space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space F i n a l space straight K. straight E. space minus space I n i t i a l space straight K. straight E. space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 half cross times 1500 space open square brackets open parentheses 50 over 3 close parentheses squared space minus space open parentheses 25 over 3 close parentheses squared close square brackets straight J space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 half cross times 1500 open parentheses 50 over 3 plus 25 over 3 close parentheses space open parentheses 50 over 3 minus 25 over 3 close parentheses straight J

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1500 over 2 cross times 75 over 3 cross times 25 over 3 straight J

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 156250 space straight J. space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space