select the correct answer.\na rocket initially at rest accelerates at a rate of 99.0 meters/second²…

select the correct answer.\na rocket initially at rest accelerates at a rate of 99.0 meters/second². calculate the distance covered by the rocket if it attains a final velocity of 445 meters/second after 4.50 seconds.\n\na. 2.50×10² meters\nb. 1.00×10³ meters\nc. 5.05×10² meters\nd. 2.00×10³ meters\ne. 1.00×10² meters

select the correct answer.\na rocket initially at rest accelerates at a rate of 99.0 meters/second². calculate the distance covered by the rocket if it attains a final velocity of 445 meters/second after 4.50 seconds.\n\na. 2.50×10² meters\nb. 1.00×10³ meters\nc. 5.05×10² meters\nd. 2.00×10³ meters\ne. 1.00×10² meters

Answer

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. Since the rocket is initially at rest, $v_{0} = 0$.

Step2: Rearrange the equation for $x$

From $v^{2}=v_{0}^{2}+2ax$ with $v_{0}=0$, we get $x=\frac{v^{2}}{2a}$.

Step3: Substitute the given values

Given $v = 445$ m/s and $a=99.0$ m/s². Then $x=\frac{(445)^{2}}{2\times99.0}=\frac{198025}{198}\approx1000$ m. In scientific - notation, $x = 1.00\times10^{3}$ m.

Answer:

B. $1.00\times 10^{3}$ meters