kinematics, integrate a to v

  • Integrate acceleration aa to obtain velocity vv v(t)v(t0)=t0ta(τ1)dτ1.(E1)\tag{E1} v(t) - v(t_0) = \int_{t_0}^t a(\tau_1) d\tau_1.
  • Initial condition v(t0)=v0v(t_0) = v_0, will give v(t)=v0+t0ta(τ1)dτ1.(E2)\tag{E2} v(t) = v_0 + \int_{t_0}^t a(\tau_1) d\tau_1.