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

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Solution

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

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

Mass $m = 1500 k g$

Work done $W = \frac{1}{2} m v^{2} - \frac{1}{2} m u^{2}$

$⟹ W = \frac{m}{2} (v^{2} - u^{2}) = \frac{1500}{2} \times ((\frac{50}{3})^{2} - (\frac{25}{3})^{2}) = 156249.97 J$

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