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

Answer

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Answer

Final Answer: $B. Between 2 and 3$

Steps

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 $t = \sqrt{\frac{2 d}{a}}$ .

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: $B. Between 2 and 3$