Drag of Car across frictionless surface.

[JosephLee]

1. a 1400 kg car with a cross section of 1.8m wide and 1.46m high slides across a frictionless surface at 19 m/s.

The question is how long does it take (in seconds) to get to 13 m/s?

the 2nd part is how long it does it take to get to 10 m/s?
2. D = .5(A)v^2 where A is the area of cross section

and basic mechanics equation V = Vo + at
3. The real problem lies in the fact that drag changes over the change in velocity. I tried solving for it initially by plugging in different velocities for the drag equation but it doesn't come out right.

So far, there is a drag force going backwards and the momentum of the car going forwards. I'm so frustrated because i believe that I am missing something very simple to solve this.

 

[tiny-tim]

Welcome to PF!

Hi Joseph! Welcome to PF!

Hint: use good ol' Newton's second law (force = rate of change of momentum) to make an equation involving t v and v/dt.

 

[baba89]

I understand your frustration in trying to solve this problem. The first step in solving this problem is to calculate the drag force on the car. This can be done using the formula D = 0.5 * (A) * v^2, where A is the area of the car's cross section and v is the velocity.

Once we have the drag force, we can use the basic mechanics equation V = Vo + at to calculate the time it takes for the car to reach a certain velocity. In this case, we are given the initial velocity (Vo = 19 m/s) and the final velocity (V = 13 m/s or 10 m/s). We can rearrange the equation to solve for time (t) and plug in the known values for Vo, V, and a (which can be calculated using the drag force and the car's mass).

However, as you mentioned, the problem lies in the fact that drag changes over the change in velocity. This means that the drag force will be different at 19 m/s compared to 13 m/s or 10 m/s. To accurately solve this problem, we would need to calculate the drag force at each velocity and use those values in our calculations. This can be done by using the formula for drag force (D = 0.5 * (A) * v^2) and substituting the different velocities.

In summary, to accurately solve this problem, we need to take into account the change in drag force as the car's velocity changes. This can be done by calculating the drag force at each velocity and using those values in our calculations to determine the time it takes for the car to reach 13 m/s and 10 m/s. I hope this helps in solving the problem.