Question

Select the correct answer. a motorist driving at 25 meters/second decelerates to 15 meters/second. the combined mass of the vehicle and the driver is 1.5 × 103 kilograms. what is the amount of mechanical work done by the vehicle? a. 7.5 × 104 joules b. 1.5 × 105 joules c. 3.0 × 105 joules d. 6.2 × 105 joules

Answer 1

The amount of mechanical work done by the vehicle is -562500 Joules, indicating work done in the opposite direction of its motion.

Step-by-step explanation:

To calculate the amount of mechanical work done by the vehicle, we can use the work-energy principle. The work done by an object is equal to the change in its kinetic energy.

Given that the initial velocity of the vehicle is 25 m/s and the final velocity is 15 m/s, we can calculate the change in kinetic energy.

Kinetic energy = 0.5 * mass * velocity²

Initial kinetic energy = 0.5 * 1500 kg * (25 m/s)²

Final kinetic energy = 0.5 * 1500 kg * (15 m/s)²

Change in kinetic energy = Final kinetic energy - Initial kinetic energy

Amount of work done = Change in kinetic energy

Substituting the values, we get:

Amount of work done = 0.5 * 1500 kg * (15 m/s)² - 0.5 * 1500 kg * (25 m/s)²

Amount of work done = 375000 Joules - 937500 Joules

Amount of work done = -562500 Joules

Since work is a scalar quantity, the negative sign indicates that the work done by the vehicle is in the opposite direction of its motion. Therefore, the correct answer is (d) 6.2 x 10⁵ joules.