Motion and Forces
Motion and Forces tests how distance, displacement, speed, velocity, acceleration and graphs describe motion, and how Newton's laws, momentum and friction explain changes in motion. Numerical questions usually need a sign convention and the correct equation of motion.
Core rules
- Distance is scalar; displacement is vector. Speed is distance/time; velocity is displacement/time. Average speed uses total distance and total time.
- Acceleration a = (v - u)/t. For uniform acceleration: v = u + at, s = ut + (1/2)at^2, and v^2 = u^2 + 2as.
- On a velocity-time graph, slope gives acceleration and area under the line gives displacement.
- Newton's first law: a body stays at rest or in uniform motion unless a net external force acts. Second law: F = ma. Third law: action and reaction are equal, opposite and act on different bodies.
- Momentum p = mv; in an isolated system total momentum is conserved. Friction opposes relative motion and produces heat.
Worked example
A 1000 kg car accelerates uniformly from rest to 20 m/s in 5 s. First a = (20 - 0)/5 = 4 m/s^2. Distance s = ut + (1/2)at^2 = 0 + (1/2)(4)(25) = 50 m. The net force is F = ma = 1000 x 4 = 4000 N. Check consistency: v^2 = u^2 + 2as gives 400 = 0 + 2(4)(50), so the distance agrees.
Traps
Do not use distance and displacement as if they are always equal. For retardation, acceleration is negative if forward is positive. Action-reaction forces do not cancel on the same body. Graph area and slope are often swapped. Include units and direction where vector quantities are asked.