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

The initial velocity \(u = 0\ m/s\), time \(t = 5.80\ s\), and displacement \(s=47.0\ m\).
Using the equation \(s = ut+\frac{1}{2}at^{2}\), substitute \(u = 0\):
\(s=\frac{1}{2}at^{2}\)
\(a=\frac{2s}{t^{2}}\)
\(a=\frac{2\times47.0}{5.80^{2}}\)
\(a=\frac{94}{33.64}\approx2.795\ m/s^{2}\)

Step2: Find the final velocity

Using the equation \(v = u+at\), substitute \(u = 0\) and \(a = 2.795\ m/s^{2}\), \(t = 5.80\ s\)
\(v=at\)
\(v=2.795\times5.80\approx16.21\ m/s\)

Step3: Convert to mph

We know that \(1\ m/s=\frac{18}{5}\ mph\)
\(v = 16.21\times\frac{18}{5}\)
\(v=\frac{291.78}{5}=58.356\ mph\)

Answer:

\(58.4\ mph\)