S = 45 meters – the path covered by the point in the last second of its movement.
It is required to determine a (m / s2) – point acceleration.
Since it is not specified in the problem statement, we assume that the point began to move without an initial speed.
Let t be the total time of point movement. Then the path traveled by the point in the last second is equal to the difference between the path that the point has traveled in time t and the path that the point has traveled in time (t-1):
S = S (t) – S (t-1) = a * t ^ 2/2 – a * (t-1) ^ 2/2 = a * t ^ 2/2 – a * (t ^ 2 – 2 * t +1) / 2 = a * t ^ 2/2 – a * t ^ 2/2 + a * t – a / 2 = a * t – a / 2 = (2 * a * t – a) / 2 = a * (2 * t – 1) / 2, hence:
a = 2 * S / (2 * t -1).
Answer: the acceleration of the body will be equal to a = 2 * S / (2 * t -1).
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