Motion in a Straight Line
Class 11 · Motion in a Straight Line

Variable Acceleration

Numerically integrate a(t) — see v(t) emerge as the integral under a(t).

Run simulation

Key Notes

01

When a = f(t), we integrate: v(t) = v₀ + ∫a(t') dt', x(t) = x₀ + ∫v(t') dt'.

02

Common cases: a = kt gives parabolic v(t); a = sin(ωt) gives oscillatory v.

03

Numerical integration (Euler, Runge–Kutta) is used when no closed form exists.

Formulas

Velocity from a(t)

Integration yields velocity.

Position from v(t)

Integration again yields position.

Important Points

Check dimensional consistency — ∫a dt has dimensions of velocity.

Variable Acceleration notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.