Question

(Serway 9th ed., 6-27) The mass of a sports car is 1200 kg. The shape of the body is such that the aerodynamic drag coefficient is 0.250 and the frontal area is 2.20 m2. Ignoring all other sources of friction, calculate the initial acceleration the car has if it has been traveling at 100 km/hr and is now shifted into neutral and allowed to coast. (Ans. 0.212 m/s2, opposite the velocity vector)

Answer 1

a = - 0.248 m/s²

Step-by-step explanation:

Frictional drag force

F = ½ *(ρ* v² * A * α)

ρ = density of air , ρ = 1.295 kg/m^3

α = drag coef , α = 0.250

v = 100 km/h x 1000m / 3600s

v = 27.77 m/s

A = 2.20m^2

So replacing numeric in the initial equation

F = ½ (1.295kg/m^3)(27.77m/s)²(2.30m^2)(0.26)

F = 298.6 N

Now knowing the force can find the acceleration

a = - F / m

a = - 298.6 N / 1200 kg

a = - 0.248 m/s²