Question

1. a runner accelerates uniformly from rest at a rate of 1.35 m/s² until she has traveled 10.0 meters. how much time did this take her?

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation $x = v_0t+\frac{1}{2}at^{2}$ is used. Since the runner starts from rest, $v_0 = 0\ m/s$. So the equation simplifies to $x=\frac{1}{2}at^{2}$.

Step2: Rearrange the equation for time

We have $x=\frac{1}{2}at^{2}$. Rearranging for $t$, we get $t=\sqrt{\frac{2x}{a}}$.

Step3: Substitute the given values

Given $x = 10.0\ m$ and $a=1.35\ m/s^{2}$. Substituting these values into the formula $t=\sqrt{\frac{2\times10.0}{1.35}}=\sqrt{\frac{20}{1.35}}\approx3.85\ s$.

Answer:

$3.85\ s$