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 85 km/h and is now shifted into neutral and is allowed to coast. (Take the density of air to be 1.295 kg/m2.)

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To calculate the initial acceleration of the car, we first need to calculate the aerodynamic drag force acting on it. The formula for drag force is given by:

F_drag = 0.5 * ρ * C_d * A * v^2

where:
F_drag = aerodynamic drag force (unknown)
ρ = air density = 1.295 kg/m²
C_d = drag coefficient = 0.250
A = frontal area = 2.30 m²
v = velocity in m/s (we'll calculate this from the given 85 km/h)

First, let's convert the car's speed to meters per second:

85 km/h * (1000 m/km) * (1 h/3600 s) = 85 * (10/36) = 850/36 ≈ 23.61 m/s

Now, we can calculate the drag force:

F_drag = 0.5 * 1.295 * 0.250 * 2.30 * (23.61)^2 = 0.5 * 1.295 * 0.250 * 2.30 * (556.4921) ≈ 89.04 N

Now that we have the drag force, we can calculate the acceleration by using Newton's 2nd Law of Motion:

F = m * a

Where:
F = force (89.04 N in this case, acting on the car)
m = mass (1200 kg)
a = acceleration (unknown)

Since the car is in neutral, the only force acting on it is the drag force, which opposes its motion. Therefore:

a = F_drag / m = 89.04 N / 1200 kg ≈ 0.0742 m/s²

However, the acceleration is negative since it opposes the direction of motion:

a = -0.0742 m/s²

So, the initial acceleration of the car is approximately -0.0742 m/s².