Question

a particle moving in 1d with constant acceleration of 10 ms2 is observed to cover a distance of 100m during 4s interval how far will the particle move in the next 4s?

Answer 1

Distance covered in next 4 seconds = distance covered in first 8 seconds - distance covered in first 4 seconds.

initial velocity of that particle =
$s = ut + \frac{1}{2} a {t}^{2} \\ 100 = 4u + \frac{1}{2} \times 10 \times {4}^{2} \\ 100 = 4u + 80 \\ 4u = 20 \\ u = 5 \: metres \: per \: second.$
distance covered in 8 seconds =
$s = ut + \frac{1}{2} a {t}^{2} \\ s = 5 \times 8 + \frac{1}{2} \times 10 \times {8}^{2} \\ s = 40 + 5 \times 64 \\ s = 40 + 320 \\ s = 360 \: metres.$
in next 4 seconds distance covered =
360 - 100 = 260 metres.

so, the distance covered in next 4 seconds = 260 m.

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