Final answer:
To determine the acceleration of an automobile, kinematic equations are used. The equation for distance covered in the n-th second relates distance, initial velocity, acceleration, and the specific second. However, without initial velocity or total time given, additional information is needed to solve for acceleration.
Step-by-step explanation:
The question concerns finding the acceleration of an automobile given that it travels a specific distance over a time interval and covers a distinct distance during a particular second. To solve this, we use kinematic equations that relate displacement, velocity, acceleration, and time. The equation for the distance covered during the n-th second is given by:
s_n = u + ½ a(2n - 1), where s_n is the distance covered during the n-th second, u is the initial velocity, a is the acceleration, and n is the second in question.
Here, we are focusing on the 6th second, so n = 6 and s_6 = 31.5 m. The equation becomes:
31.5 m = u + ½ a(2(6) - 1).
Since the initial velocity (u) is not directly given, we need another kinematic equation to relate distance travelled, initial velocity, and acceleration over the total time. The equation s = ut + ½ at², where s is the total distance, and t is the total time, can be used for the first 5 seconds, or a different approach can be applied involving the total distance covered till the 6th second to find u and then solve for a. However, additional information or formulas would be needed to definitively solve the problem as it stands.