Question

A runner starts from rest and in 2 s reaches a speed of 7 m/s. If we assume that the speed changed at a constant rate (constant net force), what was the average speed during this 2 s interval.

Answer 1

Answer:

$v=3.5\frac{m}{s}$

Explanation:

The average speed is defined as:

$v=\frac{\Delta x}{\Delta t}$

Using the equations for uniformly accelerated motion, we calculate the runner's acceleration:

$a=\frac{v_f-v_o}{2}\\a=\frac{7\frac{m}{s}-0\frac{m}{s}}{2s}\\a=3.5\frac{m}{s^2}$

Now, we can calculate the distance that the runner travels:

$\Delta x=v_0t+\frac{at^2}{2}\\\Delta x=(0\frac{m}{s})(2s)+\frac{3.5\frac{m}{s}(2s)^2}{2}\\\Delta x=7m$

Finally, we calculate the runner's average speed:

$v=\frac{7m}{2s}\\v=3.5\frac{m}{s}$