91Ó°ÊÓ

Calculating force is a fundamental concept in physics, particularly when dealing with motion and Newton's second law. The formula used is \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration. In this exercise, both car A and car B are accelerating from rest, which means they are initially stationary.
To find the net average force that acts on each car, first determine the acceleration (which remains constant in this scenario) and then use this acceleration value to compute the force.

• For car A, with a mass of 1400 kg, the force was calculated to be 4200 N.
• For car B, with a mass of 1900 kg, the force was found to be 5700 N.

The differing forces arise from the difference in mass between the two cars, demonstrating that more massive objects require greater force to achieve the same acceleration.

Acceleration is a key parameter in motion problems, especially when using Newton's second law. When objects accelerate from a standstill, determining their acceleration helps us calculate the acting force.
In this case, both cars accelerated from an initial velocity of 0 m/s to a final velocity of 27 m/s over a 9.0-second interval.
The formula to calculate acceleration is:\[ a = \frac{v_f - v_i}{t} \] where:

• \( v_f \) is the final velocity = 27 m/s
• \( v_i \) is the initial velocity = 0 m/s
• \( t \) is the time taken = 9.0 s

Substituting those values, we get:\[ a = \frac{27 \text{ m/s} - 0 \text{ m/s}}{9.0 \text{ s}} = 3 \text{ m/s}^2 \]This shows each car experiences an identical acceleration of 3 m/s², which is crucial for calculating the net average forces acting on them.

The relationship between mass and force is a core concept of Newton's second law. This relationship demonstrates how the same acceleration affects objects of different masses.
Given the formula \( F = ma \), it is evident that force is directly proportional to both mass and acceleration. When two objects experience the same acceleration, the one with more mass will require a larger force to achieve that acceleration.

• Car A, with a mass of 1400 kg, required a force of 4200 N to accelerate.
• Car B, being heavier with a mass of 1900 kg, needed 5700 N of force to reach the same acceleration.

This shows that as mass increases, the required force for the same amount of acceleration also increases. Understanding this mass-force relationship helps reinforce the principles behind calculating the force for any accelerating object.