Question

An object is initially traveling in the positive x direction with a velocity of +5m/s and an acceleration of +3m/s². At what position will it be after 8 seconds? (You may assume that it starts at x_o = 0).

Answer 1

It is the motion with constant acceleration, so $a=+3\,\mathrm{m/s}^2, \; v(t) = v_0 + at = +5\,\mathrm{m/s} + 3\,\mathrm{m/s^2}\cdot t,$

$x(t) = x_0 + v_0t + \dfrac{at^2}{2} = 0 + 5\,\mathrm{m/s}\cdot t + \dfrac{3\,\mathrm{m/s^2}\cdot t^2}{2}.$

Therefore, $x(8) = 0 + 5\,\mathrm{m/s}\cdot 8\,\mathrm{s} + \dfrac{3\,\mathrm{m/s^2}\cdot (8\,\mathrm{s})^2}{2} = 136\,\mathrm{m}.$