Final answer:
To find the initial velocity of an automobile with given acceleration and displacement, we would normally use a kinematic equation. However, additional information such as the car's final velocity or whether it stops at the end is needed to avoid an unrealistic solution that involves taking the square root of a negative number.
Step-by-step explanation:
To determine the initial velocity of an automobile given its acceleration and displacement, we use the kinematic equation:
v2 = u2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
In this scenario, the car's final velocity is not provided, but we can still solve for u despite this. Assuming the car comes to a stop at the end of its displacement, v would be 0, and the formula can be rearranged to solve for u:
u = sqrt(v2 - 2as)
u = sqrt(02 - 2(5.0 m/s2)(114m))
u = sqrt(-1140)
This equation would result in an imaginary number because of the negative inside the square root, which suggests that our initial assumption that the car comes to a stop may not be correct or more information is needed to complete this problem.
Therefore, to find the initial velocity, we need either the final velocity of the car or confirmation of whether the car stops at the end of the displacement.