Question

Example 6: If the mass of car is 200 kg. then how much work will be done to increase its velocity from 36 km/h to 72 km/h. Solution : mass of car m = 200 kg.​

Answer 1

Given,

The mass of the car = 200 kg

Initial Velocity of the car ($V_{i}$) = 36 km/h = $\frac{36000}{3600} m/s = 10 m/s$

Final Velocity of the car ($V_{f}$) = 72 km/h = $\frac{72000}{3600} m/s = 20 m/s$

To Find,

How much work will be done to increase the velocity of the car from 36 km/h to 72 km/h?

Solution,

We can easily solve this problem by applying Work-Energy Theorem. According to this theorem, "The net work done on a body is equal to change in kinetic energy of the body".

We can write this theorem as,

$K_{f} - K_{i} = W$

where,

$K_{f} =$ final kinetic energy

$K_{i} =$ initial kinetic energy

$W =$ net work done

Therefore, we can write

$W = K_{f} - K_{i} \\W = \frac{1}{2} mV_{f}^{2} - \frac{1}{2} mV_{i}^{2} \\W = \frac{1}{2} m(V_{f}^{2} - V_{i}^{2})\\W = \frac{1}{2} *200*(20^{2} - 10^{2})\\W = 30000$

Hence, the net work done, $W = 30000 J$.