AS Level Mathematics · Mechanics. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.
Kinematics describes how a particle moves along a line. Displacement, velocity and acceleration are vectors: choose one direction as positive and give the opposite direction a minus sign. Distance and speed are scalars and are never negative.
On a displacement–time graph the gradient is the velocity. On a velocity–time graph the gradient is the acceleration and the area under the graph is the displacement.
If the acceleration is constant, use the constant acceleration formulae. If s or v is given as a function of t, the acceleration is usually not constant, so you must differentiate or integrate instead.
Using the constant acceleration formulae when v or s is given as a function of t. These formulae work only when a is constant; otherwise differentiate or integrate.
Answer: 1.2 m s−2
Try each one, then open the answer.
Answer: C. s = ut + (1/2)gt2 = 0 + (1/2)(10)(9) = 45 m. 30 m s−1 is the speed on impact, not the height.
Answer: D. Car: s = 10t + t2. Motorcycle: s = 2t2. Equal displacements: 2t2 = 10t + t2, so t2 − 10t = 0 and t = 10 s (t = 0 is the start). Both are then 200 m from A.
Answer: C. At the top v = 0. v2 = u2 − 2gs: 0 = 625 − 20s, so s = 31.25 m. Forgetting the 2 in 2gs gives 62.5 m.
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