The body moves from a state of rest with uniform acceleration. How many times is the path traversed by the body

The body moves from a state of rest with uniform acceleration. How many times is the path traversed by the body in 3 seconds of movement greater than the path traversed in 2 seconds?

The path S1 covered in the first second is equal to the path taken in one second t1.
S1 = at212 (1)
But the path S2, traversed in the second second, is not equal to the path in two seconds. It can be found as the difference between the two seconds path (t1 + t2) and the one second path t1.
S2 = a (t1 + t2) 22 — at212 (2)
Let us divide expression (2) by expression (1).
S2S1 = (t1 + t2) 2 — t21t21
S2S1 = t21 + 2t1t2 + t22 — t21t21 = 2t1t2 + t22t21
Let’s count the answer:
S2S1 = 2⋅1⋅1 + 1212 = 3



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