Question

What is the work to be done to increase the velocity from 18 km/hr to 19 km/hr if the mass of the care is 2000 kg?

Answer 1

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Answer 2

Answer:

If the mass of the care is 2000 kg, the work to be done to increase the velocity from 18 km/hr to 19 km/hr will be $2854.9382 \ J$

Explanation:

We can use the work-energy theorem to solve this problem.

Work done (W) = Change in kinetic energy (Δ K.E)

W = Δ K.E                                 ...(1)

Let m be the mass and v is the velocity of the object. Then the expression for kinetic energy is given by,

Kinetic energy (K.E) = $\frac{1}{2} m V^{2}$      ...(2)

Change in K.E = $\frac{1}{2}m\ \Delta V$

Where $\Delta V = v-u$

So the equation(1) becomes,

$W = \frac{1}{2}m\times (v^{2} -u^2)$                   ...(3)

In the question, it is given that,

$m = 2000\ kg$

$v= 18\ km/h = 18\times \frac{5}{18} = 5\ m/s$

$v= 19\ km/h = 19\times \frac{5}{18} = 5.2778\ m/s$

Substitute the values into equation (2),

$W = \frac{1}{2}\times 2000\times (5.2777^2-5^2) = 2854.9382 \ J$

Thus the work done   $= 2854.9382 \ J$