← Unit 1: Kinematics
Calculus-Based Kinematics
Velocity is the derivative of position; acceleration is the derivative of velocity — and integrating acceleration or velocity recovers the other quantities.
Overview
v(t) = dx/dt, a(t) = dv/dt = d²x/dt². Given a(t), velocity is found via v(t) = v₀ + ∫a(t)dt, and position via x(t) = x₀ + ∫v(t)dt. This calculus-based approach handles non-constant acceleration that the algebra-based kinematic equations cannot.
Practice Quiz
Question 1 of 1Score so far: 0/0
An object's acceleration is a(t) = 6t. If v(0)=0, find v(t).