# The power of car engine is 500watt and mass of car is 1000Kg. Then How much time would engine take to change its momentum from $25000\ kg\ m\ s^{-1}$ to $4000\ kg\ m\ s^{-1}$

Chamge in kinetic energy is given as

$\Delta K=\frac{\Delta P^{2}}{2m}$

where P is momentum and m is mass of the body

Initial Momentum P1 = 25000 kg m s-1

Final Momentum P2 = 4000 kg m s-1

Mass of car, m = 1000 kg

$\\\Delta K=\frac{P_{2}^{2}-P_{1}^{2}}{2m}\\ \Delta K=\frac{4000^{2}-25000^{2}}{2\times 1000}\\ \Delta K=-304.5\ kJ$

Power of engine, P = 500 W

Time taken is t

$\\t=\frac{|\Delta K|}{P}\\ t=\frac{304500}{500}\\ t=609\ s$

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