Final answer:
A 1700 kg car would need to travel at approximately 139 km/h to have the same kinetic energy as a 20000 kg truck traveling at 24 km/h. The calculation involves using the kinetic energy formula and setting the energies equal to each other.
Step-by-step explanation:
To determine at what speed a 1700 kg compact car must travel to have the same kinetic energy as a 20000 kg truck going 24 km/h, we use the formula for kinetic energy (KE), which is KE = ½mv², where m is mass and v is velocity. Since the kinetic energy must be the same for both the car and the truck, we can set their formulas equal to each other and solve for the car's velocity.
For the truck moving at 24 km/h (which is equivalent to 6.67 m/s), its kinetic energy is:
KEtruck = ½ * 20000 kg * (6.67 m/s)²
For the car with an unknown speed (v), we set the kinetic energy equal to that of the truck:
½ * 1700 kg * v² = ½ * 20000 kg * (6.67 m/s)²
Solving for v, we get:
v = √((20000 kg * (6.67 m/s)²) / 1700 kg)
v = 38.58 m/s, which is approximately 139 km/h
Therefore, a 1700 kg car would need to travel at approximately 139 km/h to have the same kinetic energy as a 20000 kg truck traveling at 24 km/h.