Question

A particle moving with a constant acceleration describes in the last second

Answer 1

Explanation:

OK,

then for the first "t" seconds, it described 16/25 of the whole distance, or

s = (16/25)x = ½at² = 0.15m/s² * t² → multiply through by 25/16

x = 0.2344t²

But also we know that the whole distance was described in t + 1 s, or

x = 0.15m/s² * (t+1)²

We now have two expressions for x -- they're equal!

0.2344t² = 0.15(t² + 2t + 1) = 0.15t² + 0.3t + 0.15

0.0844t² - 0.3t - 0.15 = 0

quadratic in t; solutions at t = -0.44 s, 4 s ← only the positive root has meaning

The particle has been in motion for t + 1 = 5 s

x = ½ * 0.30m/s² * (5s)² = 3.75 m

It only SEEMS like we need more data.