Randall D. Knight — Kinematics in One Dimension: Problem Problem_40

A particle's velocity is described by the function \(v_x = kt^2 \text{ m/s}\), where \(k\) is a constant and \(t\) is in \(s\). The particle's position at \(t_0 = 0 \text{ s}\) is \(x_0 = - 9.0 \text{ m}\). At \(t_1 = 3.0 \text{ s}\), the particle is at \(x_1 = 9.0 \text{ m}\). Determine the value of the constant \(k\). Be sure to include the proper units.