91Ó°ÊÓ

Kinematic equations are a set of four equations that can predict unknown values like displacement, velocity, time, and acceleration. These equations apply only to objects moving with constant acceleration. In our exercise, bringing a car to a halt utilizes the kinematic equation:

• \( v_f^2 = v_i^2 + 2a d \)

This equation lets us find acceleration when a car comes to a stop over a certain distance. Here, we use it by knowing:

• Initial speed \( (v_i) = 15.0 \mathrm{~m/s} \)
• Final speed \( (v_f) = 0 \mathrm{~m/s} \)
• Distance \((d) = 50.0 \mathrm{~m}\)

We plug these into the equation:\[0 = (15.0)^2 + 2a \, (50.0)\]Solving gives us the required acceleration. The negative sign in acceleration indicates deceleration, meaning the car slows down.

Newton's second law of motion is a fundamental principle connecting force, mass, and acceleration. It is expressed as:

• \( F = ma \)

Where:

• \( F \) is the net force applied to an object
• \( m \) is the mass of the object
• \( a \) is the acceleration

In our problem, we use this law to find the force needed to stop the car. The given mass is \( 1580 \mathrm{~kg} \), and the acceleration calculated is \( -2.25 \mathrm{~m/s}^2 \).Plugging these values into the formula:\[F = 1580 \times (-2.25) = -3555 \, \mathrm{N}\]This result tells us the force magnitude, and the negative sign signifies direction, emphasizing that the force is opposite to the car's motion.

Net force is the total force acting on an object, considering all individual forces. It's crucial when determining how an object accelerates or decelerates. In the exercise, after finding the acceleration, we calculated the net force using what Newton described as the relationship between mass and acceleration. We determined the force required to stop the car over a set distance.The magnitude of this force is critical for understanding practical applications like brake design, ensuring a vehicle can safely and effectively stop. The calculated net force here is \( |3555 \, \mathrm{N}| \), helping us understand the stopping power needed. This concept illustrates how various forces interact and impacts our everyday life, especially in transportation and safety engineering.