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Question

What is the work to be done to increase the velocity of a car from $$30\ km\ h^{-1}$$ to $$60\ km\ h^{-1}$$ If the mass of the car is $$1500\ kg$$?


Solution

Initial velocity    $$u = 30 \ km/h = 30\times \dfrac{5}{18} = \dfrac{25}{3} \ m/s$$

Final velocity    $$v = 60 \ km/h = 60\times \dfrac{5}{18} = \dfrac{50}{3} \ m/s$$

Mass   $$m = 1500 \ kg$$

Work done   $$W = \dfrac{1}{2}mv^2 - \dfrac{1}{2}mu^2$$

$$\implies \ W = \dfrac{m}{2}(v^2-u^2)  = \dfrac{1500}{2}\times ((\dfrac{50}{3})^2 - (\dfrac{25}{3})^2) = 156187 \ J$$

Physics

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