Question

9. A runner is initially going 5 m/s to the right when she slows down to 2 m/s over 10 seconds.
a) What is her acceleration?
b) How far does she travel in these 10 seconds?

Answer 1

a) We can find her acceleration from the kinematic equation:

$$v=v_0+at,$$ $$a=\dfrac{v-v_0}{t}=\dfrac{2\ \dfrac{m}{s}-5\ \dfrac{m}{s}}{10\ s}=-0.3\ \dfrac{m}{s^2}.$$

The sign minus means that the runner slows down.

b) We can find the distance traveled by the runner from the kinematic equation:

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=5\ \dfrac{m}{s}\cdot 10\ s+\dfrac{1}{2}\cdot (-0.3\ \dfrac{m}{s^2})\cdot (10\ s)^2=35\ m.$$

Answer:

a) $a=-0.3\ \dfrac{m}{s^2}.$

b) $d=35\ m.$