This **question aims** to find the **distance a basketball player** runs from rest and **moves with speed** 6.0 m/s. The article uses an equation of motion to solve for unknown values. **Equations of motion** are mathematical formulas that describe a body’s **position**, **velocity**, or **acceleration **relative to a given frame of reference.

If the** position of an object changes** to a reference point, it is said to be in motion to that reference, whereas if it doesn’t change, it is at rest at that **reference point.** To better understand or solve different situations of rest and motion, we derive some standard equations related to the concepts of **a body’s distance**, **displacement**,** velocity**, and **acceleration **using an equation called the **equation of motion.**

**Equations of motion**

In the **situation of motion** with **uniform** or **constant acceleration** (with the same change in velocity in the same time interval), we derive the **three standard equations** of motion, also known as the laws of constant acceleration. These equations contain the quantities **displacement**(s), **velocity** (initial and final), **time**(t), and **acceleration**(s) that govern the motion of the particle. These equations can only be used when the acceleration of the body is constant, and the motion is a straight line. The **three equations** are:

**The first equation of motion:**

\[v =u+at\]

**Second equation of motion:**

\[F =ma\]

**Third equation of motion:**

\[v^{2} =u^{2}+2aS\]

**Where:**

- $m$ is the
**mass** - $F$ is the
**force** - $s$ is the
**total displacement** - $u$ is the
**initial velocity** - $v$ is the
**final velocity** - $a$ is the
**acceleration** - $t$ represents
**the time of motion**

**Expert Answer**

Since the **sprinter accelerates uniformly**, we can use the **equation of motion.** First, we need to calculate the sprinter’s acceleration using the **first** **equation of motion:**

\[v =u+at\]

$v$ is **final velocity**, and $u$ represents the **initial velocity.**

\[a = \dfrac{v-u}{t}\]

\[a = \dfrac{6-0}{1.5}\]

\[a = 4\dfrac{m}{s^{2}}\]

Now the **distance covered by the sprinter is calculated** according to the $3rd$ **equation of motion.**

\[v^{2} = u^{2} +2aS\]

**Rearrange** the equation for the unknown $S$.

\[S = \dfrac{v^{2} -u^{2}}{2a}\]

**Plug** values into the above **equation** to find the distance.

\[S =\dfrac{6^{2} -0}{2\times 4}\]

\[S = 4.5m\]

Hence, the** distance run by the sprinter** is $S=4.5m$.

**Numerical Result**

The** distance run by the sprinter** is $S=4.5m$.

**Example**

As a basketball player prepares to shoot the ball, he starts from rest and sprints at $8.0\dfrac{m}{s}$ in $2\:s$. Assuming the player accelerates uniformly, determine the distance he runs.

**Solution**

Since the **sprinter accelerates uniformly**, we can use the **equation of motion.** First, we need to calculate the sprinter’s acceleration using the **first** **equation of motion:**

\[v =u+at\]

$v$ is **final velocity,** and $u$ is the **initial velocity.**

\[a =\dfrac{v-u}{t}\]

\[a =\dfrac{8-0}{2}\]

\[a =4\dfrac{m}{s^{2}}\]

Now the **distance covered by the sprinter is calculated** according to the $3rd$ **equation of motion:**

\[v^{2} =u^{2}+2aS\]

**Rearrange** the equation for the unknown $S$.

\[S =\dfrac{v^{2}-u^{2}}{2a}\]

**Plug** values into the above **equation** to find the distance.

\[S =\dfrac{8^{2}-0}{2\times 4}\]

\[S =8m\]

Hence, the** distance run by the sprinter** is $S=8m$.