Question

A 64.1 kg runner has a speed of 4.50 m/s at one instant during a long-distance event.HINT(a)What is the runner's kinetic energy at this instant (in J)? J(b)How much net work (in J) is required to double his speed? J

Answer 1

We will have the following:

a)

$\begin{gathered} k=\frac{1}{2}(64.1kg)(4.50m/s)^2\Rightarrow k=\frac{51921}{80}J \\ \\ \Rightarrow k\approx649.01J \end{gathered}$

So, the kinetic energy is approximately 649.01 J.

b) Now, we know that if we want to double the velocity, then the work must b 4 times that of the original; thus:

$\begin{gathered} W=\frac{51921}{20}J-\frac{51921}{80}J\Rightarrow W=\frac{155763}{80}J \\ \\ \Rightarrow W\approx1947.04J \end{gathered}$

So, the net work must be approximately 1947.04J.