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ICSE Class 10 Physics 2023 Paper

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A car of mass 120 kg120\ \mathrm{kg} is moving at a speed 18 km/h\text{km/h} and it accelerates to attain a speed of 54 km/h54\ \text{km/h} in 5 seconds. Calculate :
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Question : 53 of 76
Marks: +1, -0
the work done by the engine.
Solution:  
Given : m=120 kgm=120\,\text{kg},
  u=18 km/h=18×100060×60=5 m/s\;u=18\,\text{km}/\text{h}=18 \times \frac{1000}{60 \times 60}=5\,\text{m}/\text{s}
  v=54 km/h=54×100060×60=15 m/s\;v=54\,\text{km}/\text{h}=54 \times \frac{1000}{60 \times 60}=15\,\text{m}/\text{s}
By work energy theorem,
Work done = Increase in Kinetic Energy
⇒  W  =  12mv2−12mu2\Rightarrow\;W\;=\;\frac{1}{2} m v^2 - \frac{1}{2} m u^2
⇒  W  =  12m(v2−u2)\Rightarrow\;W\;=\;\frac{1}{2} m (v^2-u^2)
⇒  W  =  12×120×(152−52)\Rightarrow\;W\;=\;\frac{1}{2} \times 120 \times (15^2-5^2)
=60×(225−25)=60 \times (225-25)
  =60×200\;=60 \times 200
  =12000 J\;=12000\,\text{J}
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