Home/Basic Physics/1D Kinematics/Velocity from variable acceleration2. 1D KinematicsVelocity from variable accelerationIn 2. 1D KinematicsFormulaCopy LaTeXv(t)=v(t0)+∫t0ta(τ) dτv(t)=v(t_0)+\int_{t_0}^{t}a(\tau)\,d\tauv(t)=v(t0)+∫t0ta(τ)dτTagskinematicskinematics 1Dphysicsphysics formulaDetailVelocity is obtained by integrating the acceleration from an initial instant.Explore the ideaExplore the ideaFound an error? Contact us.Related formulasRelatedInstantaneous velocityv=dxdtv=\frac{dx}{dt}v=dtdxOpen formulaOpen in sectionRelatedInstantaneous accelerationa=dvdt=d2xdt2a=\frac{dv}{dt}=\frac{d^2x}{dt^2}a=dtdv=dt2d2xOpen formulaOpen in sectionRelatedPosition from variable velocityx(t)=x(t0)+∫t0tv(τ) dτx(t)=x(t_0)+\int_{t_0}^{t}v(\tau)\,d\taux(t)=x(t0)+∫t0tv(τ)dτOpen formulaOpen in section