Car Racing Scenario?
Two cars, one with a mass of 1500 kg and the other with a mass of 2000 kg, are racing on a straight track with the same initial speed of 25 m/s. Assuming the cars accelerate uniformly from the starting line, compare their kinetic energies after covering a distance of 100 meters if the car with the lower mass has a higher acceleration.
1 Answer
📌 CONCEPT: The kinetic energy of an object depends on its mass and velocity, with the formula KE = ½ mv^2, where KE is kinetic energy, m is mass, and v is velocity.
📐 RULE / FORMULA: According to the formula KE = ½ mv^2, kinetic energy is directly proportional to the square of the velocity and the mass of the object.
💡 WORKED EXAMPLE: In this scenario, the car with the lower mass has a higher acceleration. Let's assume the acceleration of the 1500 kg car is a. Then, the 2000 kg car will have an acceleration of a' = v^2 / (2 × 100) = (25^2) / (2 × 100) = 3.125 m/s^2. Now, if both cars cover a distance of 100 m, their final velocities will be the same, as acceleration is uniform. Therefore, their kinetic energies will be the same, as they have the same mass and velocity.
⚠️ COMMON MISTAKE: Students often assume that the car with the higher acceleration will have more kinetic energy, but this is incorrect as the formula for kinetic energy is dependent on mass and velocity, not acceleration.
13 Aug 26
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