What work is said to be done to increase the velocity of a car from $15\ km/h$ to $30\ km/h$, if the mass of the car is $1000\ kg$?

Here as given:

Initial velocity $u=15\ km/h=15\times\frac{1000}{60\times60}=\frac{50}{12}\ m/s$      [$\because 1\ km/h=\frac{1000}{60\times60}\ m/s$]

Final velocity $v=30\ km/h=30\times\frac{1000}{60\times60}=\frac{100}{12}\ m/s$

Mass of the car $m=1000\ kg.$

Work done$=$Change in kinetic energy

$=\frac{1}{2}mv^2-\frac{1}{2}mu^2$

$=\frac{1}{2}m( v^2-u^2)$

$=\frac{1}{2}\times1000[( \frac{100}{12})^2-( \frac{50}{12})^2]$

$=500[\frac{10000}{144}-\frac{2500}{144}]$

$=500[\frac{10000-2500}{144}]$

$=500\times\frac{7500}{144}$

$=500\times52.08$

$=26,041.7\ joule$

Hence, the work done to increase the velocity of a car from $15\ km/h$ to $30\ km/h$ is $26,041.7\ joule$ 

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Updated on: 10-Oct-2022

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