Corolla vs Ferrari

Corolla vs Ferrari

Imagine racing your car against an F1 car. Your car has speed \(100~km/h\) while the F1 car has speed \((300~km/h\). The race director decides to show mercy and gives your car a head start. How long will it take for the F1 car to catch up to you?

Denote \(t_0 > 0\) as the head start given to your car. In some time \(t > t_0\), your car travels a distance \(d\) as, \[ d = 100t, \tag{1}\]

and the F1 car will travel that same distance as, \[ d = 300(t - t_0). \tag{2}\]

Substituting Equation 1 into Equation 2 and solving for \(t\) gives \[ \begin{align} 100t &= 300(t - t_0), \\ 200t &= 300t_0, \\ t &= \frac{3}{2}t_0. \end{align} \tag{3}\]

Now, let’s do a drag race! Let the drag strip be a \(1~km\) long straight. What is the head start your car requires to tie or win the race?

Substituting Equation 3 into Equation 1, we’ve \[\begin{equation} \label{eq:d} d = 150t_0. \end{equation}\] We plug in the numbers to get \(t_0 = 1/150~h = 24~s\). Therefore, your car needs to have a head start of at least \(24~s\) to tie or win.