Effects of drag on the distance of a car travelling

[oscar90]

Homework Statement

A car starts at 100 m/s and deploys a parachute. After 10 seconds its speed decreases to 45.45 m/s. Calculate the distance the car has traveled in this duration. The effects of ground resistance are ignored.

drag coefficient and planform area product (Cd * A) = 4 m^2

Homework Equations

drag force, Fd = 1/2 (rho) * u^2 * Cd * A

rho = density, 1.22 kg/m^3
u = speed
Cd = drag coefficient
A = planform area

-Fd = m du/dt

m = mass

The Attempt at a Solution

Basically I managed to calculate the speed after 10 seconds which is 45.45 m/s by integrating -Fd = m du/dt.

I cannot use the SUVAT equations to calculate the distance because it is not constant acceleration (I think). Besides, even if I try this method I get the question wrong. The answer from my lecturer is supposedly s=657m.

I think the above equation must be integrated again to get the displacement but I have tried and I think I'm missing something because I can't manipulate it so that I end up with s in the formula.

Please help as I have pulled my hair off trying to figure this out to no avail.

 

[HengHY]

What is the value for mass?

 

[oscar90]

Oops sorry forgot to put that value. Mass is 2000 kg.

 

[jack action]

From:

[tex]ma=F_d[/tex]

And:

[tex]a dx=u du[/tex]

You get:

[tex]\int dx=\int\frac{m u}{F_d}du[/tex]

 

[DeeNos]

I would first clarify the assumptions and limitations of the problem. I would ask questions such as: Is the car moving in a straight line? Is the parachute the only source of drag on the car? Are we assuming a constant drag coefficient and planform area throughout the 10 seconds? Are we ignoring any other factors that may affect the car's speed, such as air resistance or changes in mass?

Once these factors are clarified, I would approach the problem by using the equations provided and integrating them to find the displacement. Since the speed is not constant, we cannot use the basic SUVAT equations, but we can use the equation -Fd = m du/dt to find the change in velocity over time. We can then integrate this to find the displacement.

However, since the answer given by your lecturer is different from what you have calculated, there may be a mistake in your calculations or assumptions. I would suggest double-checking your work and seeking help from your lecturer or a peer if needed. It is also important to clearly show your steps and assumptions in your solution to help identify any errors.