Question

a bicyclist, initially at rest, begins pedaling and gaining speed steadily for 5.80s during which she covers 47.0m. what was her final speed (in given units)? mph

Explanation:

Step1: Find the acceleration

We use the equation \(x = v_0t+\frac{1}{2}at^{2}\). Since \(v_0 = 0\) (initially at rest), the equation simplifies to \(x=\frac{1}{2}at^{2}\).
We can solve for \(a\): \(a=\frac{2x}{t^{2}}\).
Substituting \(x = 47.0m\) and \(t = 5.80s\), we get \(a=\frac{2\times47.0}{5.80^{2}}=\frac{94}{33.64}\approx2.795m/s^{2}\).

Step2: Find the final speed

We use the equation \(v = v_0+at\). Since \(v_0 = 0\), \(v = at\).
Substituting \(a\approx2.795m/s^{2}\) and \(t = 5.80s\), we get \(v=(2.795)\times5.80 = 16.211m/s\).

Step3: Convert units to mph

We know that \(1m/s=\frac{18}{5}mph\).
So \(v = 16.211\times\frac{18}{5}mph\).
\(v=16.211\times3.6mph\approx58.4mph\)

Answer:

\(58.4mph\)