Question

a bicyclist steadily speeds up from rest to 11.0m/s during a 4.30s time interval. determine all unknowns and answer the following questions. what is the magnitude of the bicyclists acceleration? how far did the bicyclist travel during this time?

Explanation:

Step1: Calculate acceleration

Use the formula \(a=\frac{v - u}{t}\), where \(u = 0m/s\) (starts from rest), \(v=11.0m/s\), \(t = 4.30s\).
\(a=\frac{11.0 - 0}{4.30}=\frac{11.0}{4.30}\approx2.56m/s^{2}\)

Step2: Calculate distance

Use the formula \(s=ut+\frac{1}{2}at^{2}\). Since \(u = 0m/s\), the formula simplifies to \(s=\frac{1}{2}at^{2}\). Substitute \(a=\frac{11.0}{4.30}m/s^{2}\) and \(t = 4.30s\)
\(s=\frac{1}{2}\times\frac{11.0}{4.30}\times(4.30)^{2}\)
\(s=\frac{1}{2}\times11.0\times4.30 = 23.65m\)

Answer:

Acceleration: \(2.56m/s^{2}\)
Distance: \(23.65m\)