Question

question 16 of 25
when a driver presses the brake pedal, his car stops with an acceleration of -0.5 m/s². how far will the car travel while coming to a complete stop if its initial speed was 8 m/s?
a. 16 m
b. 8 m
c. 32 m
d. 64 m

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 displacement.

Step2: Determine the values of variables

The car comes to a stop, so $v = 0$. The initial speed $v_{0}=8\ m/s$ and the acceleration $a=- 0.5\ m/s^{2}$.

Step3: Rearrange the equation to solve for $x$

Starting from $v^{2}=v_{0}^{2}+2ax$, we can rewrite it as $x=\frac{v^{2}-v_{0}^{2}}{2a}$.

Step4: Substitute the values into the formula

Substitute $v = 0$, $v_{0}=8\ m/s$, and $a=-0.5\ m/s^{2}$ into the formula:
\[

$$\begin{align*} x&=\frac{0 - 8^{2}}{2\times(-0.5)}\\ &=\frac{-64}{-1}\\ &=64\ m \end{align*}$$

\]

Answer:

D. 64 m