Question

The mass of a sports car is 1000 kg. The shape of the car is such that the aerodynamic drag coefficient is 0.260 and the frontal area is 2.10 m2. Neglecting all other sources of friction, calculate the initial acceleration of the car, if it has been traveling at 90 km/h and is now shifted into neutral and is allowed to coast. (Take the density of air to be 1.295 kg/m3.)

Answer 1

`-0.221m/s^2`

Step-by-step explanation:

We are given that

Mass of car=m=1000 kg

Drag coefficient,
`C_d=0.260`

Frontal area,A=
`2.1 m^2`

Speed, v=90 km/h=
`90* (5)/(18)=25 m/s`

`1km/h=(5)/(18) m/s`

Density of air,
`\rho=1.295 kg/m^3`

We know that

Drag force,
`f_d=-(1)/(2)\rho v^2 AC_d`

`a=(f_d)/(m)`

Using the formula

`a=(-(1)/(2)* (1.295)* (25)^2* 2.1* 0.26)/(1000)=-0.221m/s^2`

Answer 2

The initial acceleration is 0,221 m/s^2.

Step-by-step explanation:

`Fcar = Fairfriction\\m*a = 0.5*A*c*density*v^2\\a = 0.5*A*c*density*v^2 / 1000 kg = 0.5*2.10m^2*0.260*1.295kg/m^3*(25 m/s)^2 / 1000 kg = 0,221 m/s^2`