The mass of a sports car is 1200 kg . The shape of the body is such that the aerodynamic drag co

step 1 So in this problem, we have a car that starts with some initial velocity and then starts to the

The mass of a sports car is 1200 kg . The shape of the body...

The mass of a sports car is 1200 $\mathrm{kg}$ . The shape of the body is such that the aerodynamic drag coefficient is 0.250 and the frontal area is $2.20 \mathrm{m}^{2} .$ Ignoring all other sources of friction, calculate the initial acceleration the car has if it has been traveling at 100 $\mathrm{km} / \mathrm{h}$ and is now shifted into neutral and allowed to coast.

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Key Concepts

Deceleration Due to Drag

The deceleration of a vehicle due to drag is determined by dividing the aerodynamic drag force by the vehicle's mass. This concept highlights how resistance forces can be translated into an acceleration (or deceleration) that affects an object's motion according to Newton’s laws.

Unit Conversion

Converting units, such as changing the speed from km/h to m/s, is essential to ensure consistency in physics calculations. Proper unit conversion is critical when using standard formulas that require SI units, particularly in dynamics and fluid resistance problems.

Aerodynamic Drag Force

Aerodynamic drag is the resistive force that opposes an object's motion through air. It is quantified by the formula F_drag = 0.5 · ? · v² · C_d · A, where ? is the air density, v is the speed of the object, C_d is the drag coefficient, and A is the frontal area. This concept is central when analyzing how air resistance decelerates moving vehicles.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = m · a). This principle is used to calculate the deceleration of an object when the net force (in this case, the drag force) acting on it is known.

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