91Ó°ÊÓ

The kinematics equation is a powerful tool in physics. It allows us to determine how an object moves under constant acceleration. When solving problems involving both deceleration and motion, we often use the kinematic equation:

• \( v^2 = v_0^2 + 2ad \)

Here, \( v \) is the final velocity, \( v_0 \) is the initial velocity, \( a \) is the acceleration (or deceleration in this case), and \( d \) is the distance. In scenarios involving a moving car coming to a stop, as in the given exercise, \( v \) becomes zero because the car isn't moving at the end.
To find how far the car travels, rearrange the equation for \( d \) as follows:

• \( d = \frac{v^2 - v_0^2}{2a} \)

This equation shows that the distance depends on the square of the initial velocity and the deceleration. When applying it, ensure consistent units—such as converting km/h to m/s for velocity—to achieve accurate results.

Newton's second law of motion is crucial for understanding how forces affect motion. It is given by the formula:

• \( F = ma \)

Where \( F \) is the force applied, \( m \) is the mass of the object, and \( a \) is the acceleration produced. In the context of a car experiencing rolling resistance, the force \( F \) is not a push or pull but a deceleration caused by resistance to motion.
When forces act on an object and cause it to slow down, such as the rolling resistance of a car, this resistance acts as a decelerating force. According to Newton's second law:

• If we set the rolling resistance force equal to \( F_r \), then \( F_r = m_{ ext{car}} \cdot a \)

We solve for \( a \), the deceleration (negative acceleration), using this formula. This law helps us understand why the car's speed decreases over time due to rolling resistance.

Calculating deceleration involves understanding how an opposing force slows down an object. Deceleration is essentially negative acceleration, indicating a decrease in speed. In the exercise, the rolling resistance serves as the deceleration force.
To calculate deceleration, first, find the rolling resistance force using:

• \( F = 0.006 \times m_{ ext{car}} \times g \)
• Given \( g = 9.81 \text{ m/s}^2 \), substituting gives us \( F_r \)

Next, use Newton's second law:

• \( a = \frac{F_r}{m_{ ext{car}}} \)
• This formula determines \( a \), showing how much the car slows down each second.

Negative values for acceleration signify slowing down. For instance, a calculated \( a = -0.05886 \text{ m/s}^2 \) tells us that the car's speed decreases by approximately 0.05886 m/s for each second it moves under rolling resistance effects.