Final answer:
To find the car's speed with the same kinetic energy as the truck, we use the kinetic energy formula and set the kinetic energies equal to each other, solving for the car's speed. The final speed of the car that gives it the same kinetic energy as a 19000 kg truck going 21 km/h is 84 km/h.
Step-by-step explanation:
To find out at what speed a 1300 kg compact car should move to have the same kinetic energy as a 19000 kg truck going 21 km/h, we can use the kinetic energy formula which is KE = ½ mv2, where m is the mass and v is the velocity of the object.
The kinetic energy of the truck is given by: KEtruck = ½ (19000 kg) * (21 km/h)2. First, we must convert the speed of the truck to m/s by multiplying by ⅖⅔: 21 km/h * (⅖⅔) = 5.83 m/s. Then we calculate KEtruck = ½ * 19000 kg * (5.83 m/s)2.
To find the speed for the car, we set the kinetic energy of the car equal to the kinetic energy of the truck:
½ * 1300 kg * v2 = ½ * 19000 kg * (5.83 m/s)2. Solving for v gives us the speed at which the car must travel to have the same kinetic energy.
By isolating v and simplifying, we find that the car's speed is much higher, due to its smaller mass. The correct answer is C. 84 km/h.