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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?
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30 votes
30 votes
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?

User Edo
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1 Answer

20 votes
20 votes

We will have the following:

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


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

Then we will have the follwing:


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

So, the work done was of 125000 Joules.

User SBF
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