Final answer:
The kinetic energy of a 910-kg automobile traveling at 87 km/h is approximately 265,807 joules, which is calculated using the formula KE = ½ mv² after converting the velocity from km/h to m/s.
Step-by-step explanation:
To calculate the kinetic energy of a 910-kg automobile traveling at 87 km/h, first convert the speed into meters per second (m/s) by dividing by 3.6 (since 1 km/h is approximately 0.27778 m/s). Therefore, 87 km/h is 24.17 m/s. The formula for kinetic energy (KE) is KE = ½ mv², where m is mass in kilograms and v is velocity in meters per second.
Plugging in the values for this problem, KE = ½ × 910 kg × (24.17 m/s)². This calculation gives us the kinetic energy in joules (J), the SI unit of energy.
KE = 0.5 × 910 kg × 584.19 m²/s² = 265,806.95 J. Therefore, the kinetic energy of the automobile is approximately 265,807 joules.