Kinematics describes motion without considering forces. It covers constant acceleration equations (SUVAT), motion graphs, free fall, and two-dimensional projectile motion.
For constant acceleration: v = u + at, s = ½(u+v)t, s = ut + ½at², v² = u² + 2as. Displacement s: change in position (vector). Distance: total path length (scalar). Velocity: rate of change of displacement. Speed: magnitude of velocity. Acceleration: rate of change of velocity (vector). Deceleration: acceleration opposite to velocity direction.
Displacement-time: gradient = velocity. Velocity-time: gradient = acceleration, area under curve = displacement. For non-uniform acceleration: gradient at a point = instantaneous value (draw tangent). Area calculated by counting squares or integration. Straight line on v-t graph = constant acceleration. Curved line = changing acceleration.
Two independent components: horizontal (constant velocity, aₓ = 0) and vertical (acceleration g downward). Horizontal: x = v₀cosθ × t. Vertical: y = v₀sinθ × t - ½gt². Time of flight: set y = 0, solve for t. Maximum height: set vᵧ = 0. Range: x at time of landing. Air resistance ignored in simple model. Path is a parabola. At any point: v = √(vₓ² + vᵧ²), direction θ = tan⁻¹(vᵧ/vₓ).
No — SUVAT equations are derived assuming constant (uniform) acceleration. If acceleration varies, you must use calculus: v = ds/dt, a = dv/dt. To find displacement from a velocity that changes non-uniformly with time, integrate: s = ∫v dt. To find velocity from varying acceleration: v = ∫a dt. In practice, if an exam question states "uniform acceleration" or gives constant values of a, use SUVAT. If it states varying acceleration or gives a = f(t), use calculus. Motion graphs also work for non-uniform acceleration (area and gradient methods).
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