1. 1 Kinematics to move describes the motion of objects Kinematics (Greek , to move) is a branch of mechanics which describes the motion of objects without the consideration of the masses or forces that bring about the motion. Kinematics studies how the position of an object changes with time Kinematics studies how the position of an object changes with time. Position / Displacement Position / Displacement is measured with respect to a set of coordinates. Velocity Velocity is the rate of change of displacement. Acceleration Acceleration is the rate of change of velocity.

2. 2 Find the velocity from the s – t graph. s / m t/s 0 4123 10 20 30 40 Velocity = slope of s – t graph = (s 2 – s 1 )/(t 2 – t 1 ) = (40 – 0)/(4 – 0) = 10 ms -1

3. 3 Find the velocity from the s – t graph. Velocity = slope of s – t graph = ? s / m t/s 0 4123 10 20 30 40 Slope of a curve? You must learn limit and differentiation.

4. 4 Limit $1100% p.a. Principal = $1Interest rate = 100% p.a. Find the total amount of money after 1 year. $ 2 $ 2.25 $ 2.44140625 $ 2.61303529 $ 2.714567475 Total amount = 1(1+1/n) n (2)Interest compounded half-yearly. (3)Interest compounded quarterly. (4)Interest compounded monthly. (5)Interest compounded daily. (1)Interest compounded yearly. Maximum amount = lim 1(1+1/n) n = 2.718281828 … = e n → ∞ n → ∞

5. 5 Slope of a curve (limit and differentiation) x y yy xx Slope at P = lim  y/  x  x → 0 = dy/dx P Q Slope is changing along a curve. i.e. slope at P ≠ slope at Q

6. 6 Velocity = rate of change of displacement Time t Displacement s ss tt Velocity = slope of s – t graph = lim  s/  t  t → 0 = ds/dt Average velocity =  s/  t

7. 7 Acceleration = rate of change of velocity Time t velocity v vv tt Acceleration = slope of v – t graph = lim  v/  t  t → 0 = dv/dt Average acceleration =  v/  t

8. 8 Summary Velocity = rate of change of displacement = ds/dt Acceleration = rate of change of velocity = dv/dt Other examples: rate of change of weight = dW/dt rate of change of volume = dV/dt

9. 9 Displacement s Time t v > 0 v = 0 v > 0 v < 0 v = 0

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11. 11 Equations for uniform acceleration a = (v – u)/t ⇒ v = u + at--- (1) Average velocity = (u + v)/2 s/t = (u + v)/2 s = (u + v)t/2 --- (2) s = (u + u + at)t/2 ⇒ s = ut + ½ at 2 --- (3) s = (u + v)[(v – u)a]/2 ⇒ 2as = v 2 – u 2 --- (4)

12. 12 Displacement = Area under v – t graph Area under v – t graph = sum of all rectangles = lim  v  t  t → 0 =∫vdt t v … tt v t1t1 t2t2 t2t2 t1t1