Final answer:
The weight of a 750 kg vehicle on Earth using the given gravitational acceleration of 10 N/kg is 7500 N. On the moon, the weight is 1250 N. The force required to accelerate the vehicle at 5 m/s² is 3750 N.
Step-by-step explanation:
If a vehicle has a mass of 750 kg on Earth, we can calculate its weight using the formula weight (w) = mass (m) × gravity (g). Given that the acceleration due to gravity on Earth is usually approximated as 9.80 m/s², the vehicle's weight would be:
w = 750 kg × 9.80 m/s² = 7350 N. However, since the question specifies to use a gravitational acceleration of 10 N/kg, the weight would be:
w = 750 kg × 10 N/kg = 7500 N on Earth.
The gravity on the moon is approximately 1/6th of Earth's gravity, so the weight of the vehicle on the moon can be calculated by dividing the weight on Earth by 6:
wmoon = 7500 N / 6 = 1250 N on the moon.
Using Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration. To find the force needed to move the vehicle with an acceleration of 5 m/s², we multiply the mass by the acceleration:
F = 750 kg × 5 m/s² = 3750 N.