Mechanics and Motion
Scalars, vectors and motion
MATSEC SEC Physics tests how motion is described and explained: distance, displacement, speed, velocity, acceleration, Newton's laws, momentum and moments.
- Distance and speed are scalars; displacement, velocity and acceleration are vectors, so direction matters.
- For uniform acceleration only: v = u + at, s = ut + ½at², v² = u² + 2as.
- Average velocity under uniform acceleration is (u + v)/2.
Forces and equilibrium
Newton's first law: zero resultant force gives constant velocity, including rest. Newton's second law: F_net = ma. Third-law pairs act on different bodies and do not cancel on one object. Weight W = mg, with g about 9.8 N/kg. Moment = force × perpendicular distance to the pivot. A body in equilibrium has zero resultant force and zero resultant moment. Momentum p = mv is conserved when no external resultant force acts. Terminal velocity is reached when drag equals weight and acceleration becomes zero.
Worked example
A car accelerates uniformly from 8.0 m/s to 20.0 m/s in 6.0 s. Find acceleration and distance.
a = (20.0 − 8.0)/6.0 = 2.0 m/s².
s = 8.0 × 6.0 + ½ × 2.0 × 6.0² = 48 + 36 = 84 m.
Check: s = ((8.0 + 20.0)/2) × 6.0 = 84 m.
Traps
Using distance for displacement when direction reverses; omitting signs for opposite directions; treating action–reaction forces as if both act on one body; using the distance along the force rather than perpendicular distance for a moment; applying suvat equations when acceleration is not constant.