# Effects of drag on the distance of a car travelling

## 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 travelled 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.

## Answers and Replies

What is the value for mass?

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

jack action
Science Advisor
Gold Member
From:

$$ma=F_d$$

And:

$$a dx=u du$$

You get:

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