Kinematics
Kinematics
Kinematics describes motion without asking what causes it. You need fluency with position, displacement, velocity and acceleration as vectors, and with the calculus links v = dx/dt and a = dv/dt; the constant-acceleration equations are valid only when a is constant, and integration is needed when it is not. Be able to read and sketch x-t, v-t and a-t graphs: the slope of x-t is velocity, the slope of v-t is acceleration, and the area under v-t is displacement. Projectile motion splits into independent horizontal (constant velocity) and vertical (constant acceleration g) parts.
Traps: confusing average with instantaneous velocity; assuming acceleration is zero at the top of a projectile's path (only the vertical velocity is zero; a = g downward throughout); reading "speeding up" as "positive acceleration" when what matters is whether velocity and acceleration point the same way; and applying constant-acceleration formulas to motion whose acceleration changes. Sign conventions and units cause many lost points.
Worked example: a ball is thrown horizontally at 12 m/s from a 20 m cliff. The vertical motion alone gives t = sqrt(2h/g) = sqrt(40/9.8) ≈ 2.0 s, so the range is x = (12)(2.0) ≈ 24 m. Launch speed does not affect fall time.
Rule of thumb: draw the velocity and acceleration arrows separately at each instant - they are not the same vector.