Question

1. a runner off the starting block accelerates at 2.0 m/s² s for 3.0 s. what is his initial displacement?

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation for displacement with initial velocity $u = 0$ (starting from rest, off the block) is $s=ut+\frac{1}{2}at^{2}$, where $s$ is displacement, $u$ is initial velocity, $a$ is acceleration and $t$ is time. Since $u = 0$, the equation simplifies to $s=\frac{1}{2}at^{2}$.

Step2: Substitute the given values

We are given that $a = 2.0\ m/s^{2}$ and $t = 3.0\ s$. Substitute these values into the equation $s=\frac{1}{2}at^{2}$. So, $s=\frac{1}{2}\times2.0\ m/s^{2}\times(3.0\ s)^{2}$.

Step3: Calculate the displacement

First, calculate $(3.0\ s)^{2}=9.0\ s^{2}$. Then, $\frac{1}{2}\times2.0\ m/s^{2}\times9.0\ s^{2}=9.0\ m$.

Answer:

$9.0\ m$