Physics problem find initial velocity

Question

Given the equation of the moving body s=3t²+2t+1 (in SI units), find its initial velocity (at t=0).

Correct answer: 2 m/s

Answer 1

Using Calculus, the velocity is ds/dt so taking the derivative of the displacement function gives the velocity function. ds/dt = 6t + 2 or v(t) = 6t + 2 and for t = 0, the velocity = 2 m/s

If you are not doing a Calculus based Physics class, you can consider the following kinematic equation:

(could be written using different variables):

x_f = x_i + v_it + 1/2at²

Notice that this is a quadratic equation (in terms of the time variable) where the "t" term has a coefficient equal to the initial velocity. Since your problem is also a quadratic function in terms of the time variable, and the "t" term has a coefficient of "2", then the initial velocity must be 2.