Question

What is the work done to increase the velocity of a car from 45km to 80 km if weight of car is 200n?

Answer 1

work = change in kinetic energy
0.5 m (v^2 - u^2)
0.5 * 1960 * [(80 * 5/1
245000

Answer 2

Answer:

If the weight of the car is 200N,  the work done to increase the velocity of a car from 45km to 80 km will be $3375.7617\ J$

Explanation:

According to the work-energy theorem,

W = ( $\Delta K.E$)

That is,

The work done (W) will be equal to the change in kinetic energy( $\Delta K.E$)

we have the expression for kinetic energy as,

$K.E = \frac{1}{2} m V^{2}$

where m-  the mass of the object

           V - velocity

If u is the initial velocity and v is the final kinetic energy then,

Initial kinetic energy = $K.E_{initial} = \frac{1}{2} m u^{2}$

Final kinetic energy = $K.E_{finall} = \frac{1}{2} m v^{2}$

Thus change in kinetic energy,   $\Delta K.E = \frac{1}{2}\ m (v^{2} -u^{2} )$   ...(1)

Given,

$u = 45\ km/h = 45\times \frac{5}{18} = 12.5 \ m/s$  

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

Weight (w) = mg =$200\ N$    ($g= 10\ m/s^2$)

              $m= \frac{200}{10} = 20\ kg$

Now, equation(1) becomes,

$\Delta K.E = \frac{1}{2}\times 20(22.222^{2} -12.5^{2} ) = 3375.7617\ J$

Thus the work done = $3375.7617\ J$