Question

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

Short answer

The speed should be 11.8 km/hr.

Step-by-step solution

Given information

20,000 kg truck going 25 km/h.

Mass of car is 1000 kg .

Explanation

The kinetic energy is calculated by

KE =1/2 (mv²) ....................................(1)

Use equation (1) to calculate the kinetic energy of car and truck and equate them

As given kinetic energy for car and truck is equal, so,

K.E_car= K.E_truck

$$\begin{gathered} K.E_{car}=0.5\times m_{car}\times v_{car}^2 \\ K.E_{truck}=0.5\times m_{truck}\times {v^2}_{truck} \\ Nowequatethem \\ 0.5\times 1000\times v_{car}^2=0.5\times 20000\times {25}^2 \\ {v}_{car}=111.804\mathrm{km}/\mathrm{h} \end{gathered}$$