The mass of a sports car is 1200 kg. The shape of the car is such that the aerodynamic drag coefficient is 0.250 and the frontal area is 2.30 m2. Neglecting all other sources of friction, calculate the initial acceleration of the car ,if it has been traveling at 80 km/h and is now shifted into neutral and is allowed to coast. (Take the density of air to be 1.295 kg/m2.)
To find the initial acceleration of the car when it is shifted into neutral and allowed to coast, we can use the equation for aerodynamic drag force:
Drag Force = 0.5 * Drag Coefficient * Density of Air * Velocity^2 * Frontal Area
First, we need to convert the velocity from km/h to m/s:
Velocity = 80 km/h * (1000 m/1 km) * (1 h/3600 s) = 22.22 m/s
Now, we can substitute the given values into the equation and solve for the drag force:
Drag Force = 0.5 * 0.250 * 1.295 kg/m^3 * (22.22 m/s)^2 * 2.30 m^2
Drag Force ≈ 110.73 N
Next, we can calculate the net force acting on the car:
Net Force = Drag Force - Frictional Force
Since the car is in neutral, there is no applied force or retarding force, so the frictional force is zero. Therefore, the net force becomes equal to the drag force.
Net Force = 110.73 N
Finally, we can use Newton's second law of motion to calculate the acceleration:
Net Force = Mass * Acceleration
Acceleration = Net Force / Mass
Acceleration = 110.73 N / 1200 kg
Acceleration ≈ 0.092 m/s^2
Therefore, the initial acceleration of the car, when shifted into neutral and allowed to coast, is approximately 0.092 m/s^2.