Problem
31. The distance, $d$, an accelerating object travels in $t$ seconds can be modeled by the equation $d=\frac{1}{2} a t^{2}$, where $a$ is the acceleration rate, in meters per second per second. If a car accelerates from a stop at the rate of 20 meters per second per second and travels a distance of 80 meters, about how many seconds did the car travel? A. Between 1 and 2 B. Between 2 and 3 C. Between 3 and 4 D. 4 E. 8
Solution
Step 1 ：Given the distance $d = 80$ meters and the acceleration $a = 20$ meters per second per second, we need to find the time $t$.
Step 2 ：We can rearrange the equation $d=\frac{1}{2} a t^{2}$ to solve for $t$, which gives us $t = \sqrt{\frac{2d}{a}}$.
Step 3 ：Substituting the given values into this equation, we get $t = \sqrt{\frac{2*80}{20}} = 2.8284271247461903$.
Step 4 ：The calculated time is approximately 2.83 seconds, which falls between 2 and 3 seconds.
Step 5 ：Final Answer: \(\boxed{\text{B. Between 2 and 3}}\)
