Linear motion questions ask you to move between displacement, velocity and acceleration using differentiation and integration. The hard part is rarely the calculus. It is deciding which step the question is asking for.
This chapter sits inside SPM Additional Mathematics and depends on differentiation and integration.
How do the parts connect?
Start with relating displacement, velocity and acceleration. Differentiating takes you from displacement to velocity to acceleration. Integrating goes the other way.
Next is finding displacement from a velocity function, where the constant of integration matters. Then distinguishing total distance from displacement and interpreting direction changes and instantaneous rest.
Method selection or routine substitution?
Take an original question. A particle moves in a straight line with velocity v = t² − 6t + 8 m/s, where t is the time in seconds. Two different questions use the same formula and need different methods.
Question A: find the velocity when t = 3. This is routine substitution. v = 9 − 18 + 8 = −1, so the particle moves at 1 m/s in the negative direction.
Question B: find when the particle is instantaneously at rest. Here you must choose to set v = 0. Then t² − 6t + 8 = 0 factorises as (t − 2)(t − 4) = 0, so t = 2 or t = 4.
A common slip in Question B is to differentiate first and set the acceleration to zero. Acceleration is a = 2t − 6, which is zero at t = 3. At that moment the velocity is −1 m/s, so the particle is moving, not resting. Zero acceleration only means the velocity has stopped changing for an instant, not that the particle has stopped.
The habit to build is to underline the quantity named in the question, then decide which of s, v or a it is, before choosing a step.
Where should you start?
If differentiating or integrating a polynomial is still slow, revisit those chapters first. Otherwise begin with the relationships lesson and move in order.
Finish with the chapter practice set. If a teacher working through unfamiliar questions at your pace would help, read about online one-to-one Additional Mathematics tuition.