Asked by Pierina Imparato on Mar 10, 2024

Verified

Find the position equation $s=21 at_{2}+v_{0}t+s_{0}$ for an object that has distance $s=24feet$ at t=1 second, $s=47feet$ at t=2 seconds, and $s=78feet$ at $t=3$ seconds.

A) $s=9t_{2}+4t+11$

B) $s=4t_{2}+11t+9$

C) $s=3t_{2}+9t+4$

D) $s=11t_{2}+4t+9$

E) $s=4t_{2}+3t+11$

A) $s=9t_{2}+4t+11$

B) $s=4t_{2}+11t+9$

C) $s=3t_{2}+9t+4$

D) $s=11t_{2}+4t+9$

E) $s=4t_{2}+3t+11$

Position Equation

A mathematical equation that describes an object's position in terms of time and other variables, often used in physics.

Distance

The length of the shortest path between two points, often measured in units such as meters or miles.

- Solve problems involving rates of change and simple interest.

Verified Answer

AD

Amy Denise Renteria

Mar 10, 2024

Final Answer :

B

Explanation :

To find the correct equation, we substitute the given values of $s$ and $t$ into the position equation $s=21 at_{2}+v_{0}t+s_{0}$ and solve for $a$ , $v_{0}$ , and $s_{0}$ . Using the given points:1. At $t=1$ , $s=24$ : $24=21 a(1)_{2}+v_{0}(1)+s_{0}$ 2. At $t=2$ , $s=47$ : $47=21 a(2)_{2}+v_{0}(2)+s_{0}$ 3. At $t=3$ , $s=78$ : $78=21 a(3)_{2}+v_{0}(3)+s_{0}$ Solving these equations simultaneously for $a$ , $v_{0}$ , and $s_{0}$ will give us the values that fit one of the given options. The correct values that fit these conditions are $a=8$ , $v_{0}=11$ , and $s_{0}=9$ , which corresponds to the equation $s=4t_{2}+11t+9$ , making option B the correct choice.

## Learning Objectives

- Solve problems involving rates of change and simple interest.