Answer:
The roadrunner will take approximately 5.285 seconds to catch up to the rattlesnake.
Explanation:
From the statement we notice that:
1) Rattlesnake moves a constant speed (
), whereas the roadrunner accelerates uniformly from rest. (
, 
)
2) Initial distance between the roadrunner and rattlesnake is 10 meters. (
, 
)
3) The roadrunner catches up to the snake at the end. (
)
Now we construct kinematic expression for each animal:
Rattlesnake
Where:
- Initial position of the rattlesnake, measured in meters.
- Final position of the rattlesnake, measured in meters.
- Speed of the rattlesnake, measured in meters per second.
- Time, measured in seconds.
Roadrunner
Where:
- Initial position of the roadrunner, measured in meters.
- Final position of the roadrunner, measured in meters.
- Initial speed of the roadrunner, measured in meters per second.
- Acceleration of the roadrunner, measured in meters per square second.
- Time, measured in seconds.
By eliminating the final positions of both creatures, we get the resulting quadratic function:
If we know that , , , and , the resulting expression is:
We can find its root via Quadratic Formula:
Roots are 
and 
, respectively. Both are valid mathematically, but only the first one is valid physically. Hence, the roadrunner will take approximately 5.285 seconds to catch up to the rattlesnake.
