Given:
Mass of car = 1000 kg
Mass of truck = 20000 kg
Speed of truck = 25 km/h
Let's find the speed at which the car will have the same kinetic energy as the truck.
We have:
[tex]KE_{car}=KE_{truck}[/tex]Apply the formula for kinetic energy:
[tex]KE=\frac{1}{2}mv^2[/tex]Thus, we have:
[tex]\frac{1}{2}m_1*v_1^2=\frac{1}{2}m_2*v_2^2[/tex]Where:
m1 is the mass of car = 1000 kg
v1 is the speed of car
m2 is the mass of truck = 20000 kg
v2 is the speed of truck = 25 km/h
Input values into the formula and solve for v1:
[tex]\begin{gathered} \frac{1}{2}*1000*v_1^2=\frac{1}{2}*20000*25^2 \\ \\ 500v_1^2=6250000 \end{gathered}[/tex]Divide both sides by 500:
[tex]\begin{gathered} \frac{500v_1^2}{500}=\frac{6250000}{500} \\ \\ v_1^2=12500 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{v_1^2}=\sqrt{12500} \\ \\ v_1=111.8\text{ km/h} \end{gathered}[/tex]Therefore, the speed of the car must be 111.8 km/h
ANSWER:
111.8 km/h