A sports car accelerates from a stop to \(100 \mathrm{km} / \mathrm{h}\) in 4 seconds. a. What is its acceleration? b. If it went from \(100 \mathrm{km} / \mathrm{h}\) to a stop in 5 seconds, what would be its acceleration? c. Suppose the car has a mass of 1,200 kg. How strong is the force on the car? d. What supplies the "push" that accelerates the car?

Kinematics is the branch of mechanics that deals with the motion of objects without considering the causes of this motion. It focuses on quantities like displacement, velocity, and acceleration.
In the given exercise, calculating acceleration involves using the formula: \[ a = \frac{\Delta v}{\Delta t} \] where:
• \(\Delta v\) is the change in velocity
• \(\Delta t\) is the change in time
Kinematics is helpful when we want to predict future position or velocity based on initial conditions and observed accelerations.
In this problem:
• Part a asks for the car's acceleration when it speeds up from 0 to 100 km/h.
• Part b asks for the car's deceleration when it slows down from 100 km/h to a stop.
Understanding these basic principles allows us to analyze the car's motion more comprehensively.

Newton's second law of motion states that the force acting on an object is equal to the mass of that object times its acceleration.
This is expressed mathematically as: \[ F = m \cdot a \] where:
• \(F\) is the force
• \(m\) is the mass
• \(a\) is the acceleration
In the exercise, we use this formula in part c to calculate the force exerted on the car. Knowing the car's mass (1200 kg) and previously calculated acceleration (6.945 m/s²), we can determine the force:
\[ F = 1200 \text{ kg} \cdot 6.945 \text{ m/s}^2 = 8334 \text{ N} \]
This shows how the car's mass and acceleration work together to result in a specific force, which is a direct application of Newton's Second Law.

Force and motion are related concepts in physics, encapsulated in Newton's Laws of Motion. A force is any interaction that, when unopposed, will change the motion of an object.
There are different types of forces that can act on an object, such as gravitational force, frictional force, and applied force.
In this exercise, the 'push' or applied force that accelerates the car comes from its engine. The engine converts energy from fuel into mechanical energy, ultimately exerting a force on the car's wheels through the drivetrain.
Effective force application results in motion, as observed in the steps where the car accelerates or decelerates over time. Motion changes due to forces can be understood in terms of acceleration, which is a measure of how quickly velocity changes. This ties back into the initial kinematic calculations and Newton's second law!

Unit conversion is a critical skill in physics to ensure all quantities are in compatible units for calculations. In our exercise, the speed is initially given in km/h, and we need to convert it to m/s for calculation purposes.
The conversion factor from km/h to m/s is: \[ \text{Speed (m/s)} = \frac{\text{Speed (km/h)} \times 1000}{3600} \]
Using this, we convert 100 km/h to m/s:
•\[ 100 \text{km/h}\ = \frac{100 \times 1000 }{3600} \text{ m/s} \approx 27.78 \text{ m/s} \]
Likewise, accurately converting units ensures the correctness of further kinematic and dynamic calculations. It aligns different physical quantities to a standard measurement, making the entire process more seamless and scientifically accurate.