Question

At what speed does a 1000 kg compact car have the same kineticenergy as a 20,000 kg truck going 25 km/h?

Answer 1

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:

`KE_(car)=KE_(truck)`

Apply the formula for kinetic energy:

`KE=(1)/(2)mv^2`

Thus, we have:

`(1)/(2)m_1*v_1^2=(1)/(2)m_2*v_2^2`

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:

`\begin{gathered} (1)/(2)*1000*v_1^2=(1)/(2)*20000*25^2 \\ \\ 500v_1^2=6250000 \end{gathered}`

Divide both sides by 500:

`\begin{gathered} (500v_1^2)/(500)=(6250000)/(500) \\ \\ v_1^2=12500 \end{gathered}`

Take the square root of both sides:

`\begin{gathered} √(v_1^2)=√(12500) \\ \\ v_1=111.8\text{ km/h} \end{gathered}`

Therefore, the speed of the car must be 111.8 km/h

ANSWER:

111.8 km/h