1 Kinematics Lesson Two Graphical Representations Equations of Motion

2 LESSON TWO LESSON OBJECTIVES What are the relationships between the s-t, v-t and a-t graphs? What are the equations of motion? When can we use the equations of motion?

3 ?? Question ?? Question : Can I define downwards as positive or leftwards as positive instead? Yes, you may if it is more convenient in the problem. Always state clearly the convention you have adopted Wrong spelling in notes

4 CASE 1: Acceleration –ve and velocity +ve +ve t = 0 s v = +20 ms -1 a = 10 ms -2 t = 1s v = +10 ms -1 In this case, the car is slowing down

5 Question +ve t = 0 s v = -20 ms -1 a = - 10 ms -2 t = 1 s v = -30 ms -1 In this case, the car is speeding down CASE 2: Acceleration –ve and velocity -ve

6 Question When the acceleration of the object is -10 m/s 2 ? Is the object accelerating or decelerating? Answer: It depends on which direction the object is moving!

7 The velocity of an object at any instant of time is given by Displacement vs. Time Graph GETTING VELOCITY Pg 10 The velocity of the object at any time is THE SLOPE (OR GRADIENT) Of the tangent line of the s-t graph at that instant in time s t1t1 t s1s1

8 The acceleration of the object at any instant in time is given by Velocity vs. Time Graph GETTING ACCELERATION Pg 10 t1t1 v t v1v1 The acceleration of the object at any time is THE SLOPE (OR GRADIENT) of the tangent line of the v-t graph at that instant of time.

9 What is the change in displacement of the object btwn t 1 and t 2 ? Velocity vs. Time Graph GETTING DISPLACEMENT t1t1 v t t2t2 Area under a velocity-time curve gives the change in displacement. Pg 10

10 Acceleration vs. Time Graph GETTING VELOCITY t1t1 a t t2t2 Area under a acceleration-time curve gives the change in velocity. Pg 11

11 SUMMARY OF RELATIONS AMONG s-t, v-t and a-t GRAPHS Pg 11 DISPLACEMENT, s VELOCITY, v ACCELERATION, a Velocity = gradient of s -t graph Acceleration = gradient of v -t graph  Change in displacement = area under v -t graph  Change in velocity = area under a -t graph

12 Equations of Motion Consider an object moving in a straight line with uniform acceleration. v t = 0 s t u s a Pg 12

13 Since acceleration is uniform, Equations of Motion t Pg 12

14 v t = 0 s t u s a Since acceleration is uniform, a = v - u t Equations of Motion Pg 12

15 Equations of Motion v = u + at 1 2 s = ut + ½ at 2 3 v 2 = u 2 + 2as Pg 13 Note: When s = 0 at t = 0. a is constant equations are vector equations

16 Equations of Motion v = u + at 1 2 s = ut + ½ at 2 3 v 2 = u 2 + 2as You are expected to memorise the equations of motion as well as know how to derive them! Pg 13

17 Graphical Representation of Equations of Motion CASE 1 (u= 0, a is +ve) Pg 13

18 Graphical Representation of Equations of Motion CASE 2 (u> 0, a is +ve) Pg 13 u

19 Graphical Representation of Equations of Motion CASE 3 (u< 0, a is +ve) Pg 13 u t1t1 t1t1 (t=0)

20 END OF LESSON 2 THANK YOU!