Question

What is the work to be done to increase the velocity of a car from 30 km per hour to 60 km per hour if the mass of the car is 1500 kg?

Answer 1

Mass of the car is m = 1500kg.
The initial velocity of the car is u = 30 km/hr.

As we know,

$WD=\Delta KE$

$=\frac{1}{2}m(v_f^2-v_i^2)$

$=\frac{1}{2}\left(1500\right)\{{\left(60\right)}^2-{\left(30\right)}^2\}$

$=\frac{1500}{2}\{{(2\times 30)}^2-{30}^2\}$

$=\frac{1500}{2}\times {30}^2\times (4-1)$

$=\frac{1500}{2}\left(900\right)\left(\frac{25}{324}\right)\left(3\right)$

$=1.56\times {10}^{5}J$

If you are a beginner then you can also use the alternative method, as follow

u = initial velocity

Similarly, final velocity is v =

With the mass and velocities, we can find the initial and final kinetic energies.

Initial Kinetic Energy = 12mu2\frac 12 mu^221​mu2

Final Kinetic Energy = 12mv2\frac 12 mv^221​mv2

The difference in these values would give us the amount of work done.

Work done = W = Change in kinetic energy = Final kinetic energy - Initial kinetic energy

W = 208416.675 J -52166.7 J

W = 156249.975 J.