Final answer:
Using the kinetic energy formula, the kinetic energy of a 910-kg automobile traveling at 87 km/h is approximately 2.65 × 105 J, which is closest to 2.46 × 105 J. The correct answer is b) 2.46 × 10^5 J.
Step-by-step explanation:
To calculate the kinetic energy of an automobile, we use the kinetic energy formula KE = ½mv2, where m is the mass of the object and v is the velocity of the object.
In this case, the mass of the automobile is 910 kg and the velocity must first be converted from km/h to m/s before substituting into the equation. The conversion factor of 1 km/h to m/s is approximately 0.27778, so the velocity 87 km/h is equivalent to 87 × 0.27778 ≈ 24.18 m/s. Now we can calculate kinetic energy:
KE = ½ × 910 kg × (24.18 m/s)2
KE = 455 × 583.7124
KE = 265691.42 J
Thus, the kinetic energy of the automobile is approximately 2.65 × 105 J, which is closest to option b) 2.46 × 105 J.