Answer
The speed of the block 3.40 meters down the incline is 2.7 m/s
Work Step by Step
Note that 3.40 m is half of 6.80 m.
Let $v_2 = 3.80~m/s$ and let $x_2 = 6.80~m$
$v_2^2 = 2ax_2$
$v_2 = \sqrt{2ax_2}$
Let $v_1$ be the speed at $3.40~m$ and let $x_1 = 3.40~m$
$v_1 = \sqrt{2ax_1} = \sqrt{2a(x_2/2)} = \frac{1}{\sqrt{2}}\sqrt{2ax_2}$
$v_1 = \frac{v_2}{\sqrt{2}} = \frac{3.80~m/s}{\sqrt{2}}$
$v_1 = 2.7~m/s$
The speed of the block 3.40 meters down the incline is 2.7 m/s
