Lesson 8 of 9 · 6 min
Using calculus in kinematics
NCERT § "Kinematic Equations for Uniformly Accelerated Motion"
When acceleration is not constant, the three equations stop working. Calculus never does.
The lesson in notes
In short
Velocity is the time derivative of position and acceleration is the time derivative of velocity.
Going the other way, displacement is the time integral of velocity and change in velocity is the time integral of acceleration.
For motion given as x(t), the body turns around where v = dx/dt = 0; path length over an interval must be added piecewise between turning points.
When acceleration depends on time, integrate directly instead of using the constant-acceleration equations.
The kinematic equations stay valid for any sign of constant acceleration, including deceleration, as long as the sign is put in consistently.