What is the work to be done to increase the velocity of a car from 30 km h–1 to 60 km h–1 if the mass of the car is 1500 kg?

Respuesta :

We will have the following:

First, we convert the velocities to m/s, that is:

[tex]\begin{cases}v_1=30\frac{km}{h}\cdot\frac{1000m}{1\operatorname{km}}\cdot\frac{1h}{60m}\cdot\frac{1m}{60s}\Rightarrow v_1=\frac{25}{3}m/s \\ \\ v_2=60\frac{\operatorname{km}}{h}\cdot\frac{1000m}{1\operatorname{km}}\cdot\frac{1h}{60m}\cdot\frac{1m}{60s}\Rightarrow v_2=\frac{50}{3}m/s\end{cases}_{}[/tex]

Then we will have the follwing:

[tex]W=\frac{1}{2}mv^2_f-\frac{1}{2}mv^2_i\Rightarrow W=\frac{1}{2}(1200\operatorname{kg})(\frac{50}{3}m/s)^2-\frac{1}{2}(1200\operatorname{kg})(\frac{25}{3}m/s)^2[/tex][tex]\Rightarrow W=125000\operatorname{kg}\cdot m^2/s^2\Rightarrow W=125000J[/tex]

So, the work done was of 125000 Joules.