A-Level Further Maths · Further Mechanics
Differential Motion
What is it
Differential motion applies calculus directly to mechanics problems where acceleration or force varies with time, position, or velocity — rather than being constant, requiring differential equations to solve for motion.
Why it matters
Real-world motion is rarely at constant acceleration — resistance forces that depend on speed, or forces that change with position, require calculus-based methods rather than the SUVAT equations used for simpler A-Level mechanics problems.
Exam tip
Identify from the outset whether the problem gives you acceleration in terms of time (integrate to get velocity) or in terms of velocity or position (a different technique using a·da/dx or a·dv/dt is needed) — misidentifying this is the most common starting error.
Related topics
Want help mastering Differential Motion?
Tell us about the student's goals and confidence — we'll design a personalised plan.