Question

what is the work to be done to increase the velocity of a car from 40 km /h to 80km /h if the mass of the car is 1000 kg? ​

Answer 1

Answer:

W = 185.185 KJ

Explanation:

initial velocity = u = 40 * 1000/3600 = 100 / 9 m/s

final velocity = v = 80 * 1000/3600 = 200 / 9 m/ s

W = 1/2 (m) (v^2 - u^2)

W = 1/2(1000)((100/9)^2 - (200/9)^2)

= 10000/54 KJ

= 185.185 KJ

Answer 2

Answer:

If the mass of the car is 1000 kg, the work done to increase the velocity of the car from 40km/h to 80km/h will be $185184.8148\ J$

Explanation:

According to the work-energy theorem,

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

Where W is the work done and Δ K.E is the change in kinetic energy.

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 $\Delta V = v-u$

u - initial velocity

v- final velocity

So the equation(1) becomes,

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

In the question, it is given that,

$m = 1000\ kg$

$u= 40\ km/h = 40\times \frac{5}{18} = 11.1111\ m/s$

$v= 80\ km/h = 80\times \frac{5}{18} = 22.2222\ m/s$

Substitute the values into equation (2),

$W = \frac{1}{2}\times 1000\times (22.2222^2-16.6666^2) = 185184.8148\ J$

Thus the work done   $185184.8148\ J$