Understanding the Concepts
* Newton's Second Law: The fundamental principle we'll use is Newton's Second Law of Motion: Force (F) = Mass (m) * Acceleration (a)
* Acceleration: Acceleration is the rate of change of velocity. In this case, the car is increasing its velocity.
* Velocity: We need to convert the given speeds from miles per hour (mph) to meters per second (m/s) for consistency with standard units.
Calculations
1. Convert Speeds to m/s:
* 30 mph = 13.41 m/s (approximately)
* 40 mph = 17.88 m/s (approximately)
2. Calculate Acceleration:
* Acceleration (a) = (Final Velocity - Initial Velocity) / Time
* We don't have the time it takes for the acceleration, so we'll leave it as a variable (t).
* a = (17.88 m/s - 13.41 m/s) / t = 4.47/t m/s²
3. Net Force Expression:
* Using Newton's Second Law: F = m * a
* Substituting the acceleration: F = m * (4.47/t) Newtons
The Expression
The expression for the net force causing the acceleration is: F = m * (4.47/t) Newtons, where:
* F is the net force in Newtons
* m is the mass of the car in kilograms
* t is the time taken to accelerate in seconds
Important Note: This expression assumes the acceleration is constant. In reality, the force might vary during the acceleration process.
