Question

a runner starts from rest and runs for one minute accelerating at 2m/s^2.
a) what is the initial velocity?
b) what is her velocity at one minute?
c) how far does she run in one minute?

Explanation:

a) Initial velocity

The runner starts from rest. By definition, initial velocity \(u = 0\space m/s\).

b) Velocity at one minute

Step1: Convert time

One minute \(t=60\space s\).

Step2: Use velocity - time formula

The formula \(v = u+at\). Given \(u = 0\space m/s\), \(a = 2\space m/s^{2}\), \(t = 60\space s\).
Substitute values: \(v=0 + 2\times60\).
\(v = 120\space m/s\).

c) Distance run in one minute

Step1: Use displacement - time formula

The formula \(s=ut+\frac{1}{2}at^{2}\). Since \(u = 0\space m/s\), the formula simplifies to \(s=\frac{1}{2}at^{2}\).

Step2: Substitute values

\(a = 2\space m/s^{2}\), \(t = 60\space s\).
\(s=\frac{1}{2}\times2\times60^{2}\).
\(s= 3600\space m\).

Answer:

a) \(0\space m/s\)
b) \(120\space m/s\)
c) \(3600\space m\)