91Ó°ÊÓ

Newton's Second Law is a fundamental principle in physics that states force is equal to mass times acceleration. This can be written as: \[ F = m \times a \] This law helps to understand how different forces act on objects to change their state of motion. In our exercise, this law allows us to calculate the force exerted by the seat belt on the driver by knowing the mass of the driver and the rate of deceleration. By multiplying the driver's mass (100 kg) by the deceleration (4.167 m/s²), we arrive at the force exerted on the driver.

Unit conversion is the process of converting a measurement from one unit to another. It is essential in physics to ensure consistency and accuracy in calculations. In our exercise, we convert the car's initial velocity from kilometers per hour (km/h) to meters per second (m/s). This is crucial because the standard unit for velocity in physics SI units is meters per second (m/s).To convert 1.5 km/h to m/s, we use the fact that 1 km/h equals 1000 meters divided by 3600 seconds:\[ 1.5 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = 0.4167 \text{ m/s} \] This conversion allows us to use the same units consistently when applying formulas and calculating deceleration.

Acceleration due to gravity, denoted as \( g \), is the acceleration that objects experience when falling freely under the influence of Earth's gravity. Its standard value is approximately 9.8 m/s². In our exercise, once we calculate the car's deceleration as 4.167 m/s², we express it in terms of the acceleration due to gravity to provide a more intuitive understanding.Expressing deceleration as a multiple of \( g \):\[ a_g = \frac{a}{g} = \frac{4.167 \text{ m/s}^2}{9.8 \text{ m/s}^2} \ a_g \ \approx 0.425 \ \]This means the deceleration is approximately 0.425 times the standard acceleration due to gravity.

Kinematics is the branch of physics that deals with the motion of objects without considering the forces causing the motion. It includes the study of speed, velocity, and acceleration. In our exercise, we calculate deceleration using kinematic equations.The formula for acceleration (or deceleration) when initial velocity \(v_i\), final velocity \(v_f\), and time \( \Delta t \) are known is:\[ a = \frac{\bigtriangleup v}{\bigtriangleup t} = \frac{v_f - v_i}{\bigtriangleup t} \] Here, the initial velocity \(v_i\) is 0.4167 m/s, the final velocity \(v_f\) is 0 m/s (since the car comes to a stop), and the time \( \Delta t \) is 0.1 seconds. Substituting these values into the formula gives us:\[ a = \frac{0 \text{ m/s} - 0.4167 \text{ m/s}}{0.1 \text{ s}} = -4.167 \text{ m/s}^2 \]This negative sign indicates deceleration, showing how quickly the car slows down.