Question

calculate the initial velocity of an object displaced 33 meters while accelerating 8 m/s^2 to a final velocity of 68 m/s how do i figure it out?

Answer 1

Use the equation

${v_f}^2-{v_i}^2=2a\Delta x$

The final velocity $v_f$ is 68 m/s, the acceleration $a$ is 8 m/s^2, and the net displacement $\Delta x$ is 33 m, so you can solve for the initial velocity $v_i$:

$\left(68\,\dfrac{\mathrm m}{\mathrm s}\right)^2-{v_i}^2=2\left(8\,\dfrac{\mathrm m}{\mathrm s^2}\right)(33\,\mathrm m)$

${v_i}^2=4096\,\dfrac{\mathrm m^2}{\mathrm s^2}$

$v_i=64\,\dfrac{\mathrm m}{\mathrm s}$