# Effects of drag on the distance of a car travelling

• oscar90
So:x=\frac{m u^2}{2 F_d}+CAt t=0, x=0, so:x=\frac{m u^2}{2 F_d}At t=10 s, u=45.45 m/s, so:x=\frac{2000*45.45^2}{2*F_d}=657 mIn summary, to calculate the distance traveled by a car with initial speed of 100 m/s and deploying a parachute after 10 seconds, the equation -Fd = m du/dt can be integrated to get the displacement formula x=\frac{m u^2}{2 F_d}. With the given values of mass and initial speed, the resulting

## 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.

What is the value for mass?

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

From:

$$ma=F_d$$

And:

$$a dx=u du$$

You get:

$$\int dx=\int\frac{m u}{F_d}du$$