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Critical problem related to acceleration

A body travels 100m in the first 2seconds and 104m in the next 4seconds.How far will it move in the next 4seconds if the acceleration is uniform?

Using the formula $D = v_o t+ \frac 1 2 a t^2$ you have two equations in two unknowns:

1) $D_1 = 100 = v_o (4) + \frac 1 2 a (4^2)$

2) $D_2 = D_1 + 100 = 204 = v_o (8) + \frac 1 2 a (8^2)$

Solve for $v_o$ and $a$ , then find the distance travelled in 12 seconds:

3) $D_3 = v_o (12) + \frac 1 2 a (12^2)$

The distance travelled between 8 and 12 seconds is then $D_3 - D_2$ .

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