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Kinematics The Equations of Motion

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Equations of Motion The equations of motion all apply to a body moving… 1.…with constant acceleration 2.…in a straight line. They can also be applied to projectile motion.

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1. The average velocity equation: We know that if an object accelerates uniformly from an initial velocity (u) to a final velocity (v) over a time (t) then… If it has travelled through a displacement (s) then also… So… Or… Average velocity = u + v 2 Average velocity = s t s = u + v t 2 s = ½ (u + v) t a

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2. The acceleration equation We know that acceleration is given by… Rearranging gives… Acceleration = v - u t v = u + at b

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3. The displacement equation Substituting b into a gives… So… s = ½ (u + u + at) t s = ½ (2u + at) t s = ut + ½ at 2 c

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The fourth equation Rearranging a gives… Substituting into b gives… Rearranging… t = 2s (u+v) v = u + a 2s (u+v) v-u = 2as (u+v) So… Expand the brackets… Simplifies to… (v–u) (u+v) = 2as uv + v 2 – u 2 – uv = 2as v 2 = u 2 + 2as d

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Note: When recalling the equations of motion, check for homogeneity if youre not sure. e.g. s = ut + ½ at 2

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Question First watch this video.this video Now, analyse the video to determine… - fall time - height of cliff - velocity upon impact

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