5. a car initially traveling at +7.0 m/s accelerates uniformly at the rate of +0.80 m/s² for a distance of…

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v^{2}=v_{0}^{2}+2ax$, where $v$ is the final velocity, $v_{0}$ is the initial velocity, $a$ is the acceleration and $x$ is the distance.

Step2: Substitute the given values

Given $v_{0}=7.0\ m/s$, $a = 0.30\ m/s^{2}$ and $x = 245\ m$. [v^{2}=(7.0)^{2}+2\times0.30\times245] [v^{2}=49 + 147] [v^{2}=196]

Step3: Solve for $v$

Take the square - root of both sides. Since velocity is a physical quantity, we consider the positive root (assuming motion in the positive direction). [v=\sqrt{196}=14\ m/s]

Answer:

$14\ m/s$