Mech Yr 2 Chapter 8 Further Kinematics jfrosttiffin

Mech. Yr 2 Chapter 8 : : Further Kinematics jfrost@tiffin. kingston. sch. uk www. drfrostmaths. com @Dr. Frost. Maths Last modified: 4 th August 2018

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Overview 1: : Vector equations for motion. 2: : Variable acceleration with vectors. 3: : Integration with vectors to find velocity/displacement Note for teachers: The first item was in the old M 1 with projectile motion in M 2. Variable acceleration was in M 2.

Vector motion After after 2 seconds? ? Fro Note: I don’t really remember as a formula as such though, but as ‘common sense’ using the reasoning above. Fro Note II: Further Mathematicians who have finished Vectors in Core Pure Yr 1 may see the similarities with vector equations of straight lines.

Example a ? b ?

? ? a b ? Remember that speed is the scalar for of velocity, so find magnitude of the vector. ? The velocity vector gives the direction of motion. Just draw it out to establish angles.

Further Example c a ? ? d b ? ?

Test Your Understanding Edexcel M 1(Old) May 2013(R) Q 6 ? ? ?

Exercise 8 A Pearson Stats/Mechanics Year 2 Pages 162 -164

Vector methods for projectiles Previously we considered the initial speed of the projectile and the angle of projection. But we could also use a velocity vector to represent the initial projection (vectors have both direction and magnitude) and subsequent motion. a ? b ? c ?

Test Your Understanding Edexcel M 2(Old) Jan 2012 Q 7 ? ? ?

Exercise 8 B Pearson Stats/Mechanics Year 2 Pages 166 -167

Variable Acceleration in One Dimension a ? b Remember with ‘reverse chain rule’, we divide by constant in front of variable. ? c Finding area under velocity-time graph. ? Can tidy up integral by factorising out common factor.

Test Your Understanding a ? b ?

Exercise 8 C Pearson Stats/Mechanics Year 2 Pages 168 -170

Differentiating Vectors ? a ? b c ? ?

Exercise 8 D Pearson Stats/Mechanics Year 2 Pages 171 -173

Integrating Vectors The constant of integration is a vector. ?

Further Example b a ? ?

Test Your Understanding Edexcel M 2(Old) Jan 2013 Q 4 ? ? ?

Exercise 8 E Pearson Stats/Mechanics Year 2 Pages 175 -176

You have reached the end of maths. * * At A Level.