 # Kinematics. Lesson Structure Part 1 – Instantaneous Speed vs Average Speed – Scalars vs Vectors – acceleration Part 2: Displacement-Time Graphs – Uniform.

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Kinematics

Lesson Structure Part 1 – Instantaneous Speed vs Average Speed – Scalars vs Vectors – acceleration Part 2: Displacement-Time Graphs – Uniform Velocity – Non-Uniform velocity Part 3: Velocity-Time Graphs – Uniform Acceleration – Non-uniform Acceleration – Finding displacement from v-t graphs

Introduction Kinematics is the study of moving objects In the previous lesson you have been introduced to physical quantities, and studied 4 of them In this topic, we will be investigating how 6 quantities interact with each other in moving objects: distance, displacement, speed, velocity, time, acceleration

Speed Speed is the measure of how fast or how slow an object moves Units: ms -1, kmh -1 Previously, you’ve learned that speed = distance / time Is this the only way to understand speed?

The fastest man on Earth Usain Bolt’s fastest time for the 100 m race is 9.58 s (2009 IAAF Championships in Berlin) What was his speed? Speed = distance/time 100/ 9.572 = 10.4 ms -1 “Usain Bolt is the fastest man on Earth (ever), so it is not humanly possible to go faster than 10.4 ms -1. “ Do you agree with this statement?

The fastest man on Earth Look at the breakdown of Bolt’s run: Usain Bolt actually reached a top speed of 12.4 ms -1, faster than the 10.4 ms -1 we mentioned previously! Time /sSpeed/ms-1 0 to 20 m2.896.92 20 to 40 m1.7511.4 40 to 60 m1.6712.0 60 to 80 m1.6112.4 80 to 100 m1.6612.0 Total9.5810.4

Instanteous Speed vs Average Speed There are two different ways to talk about speed: instantaneous speed or average speed Instantanous speed is how fast an object is moving at that instant in time Average Speed is given by the formula Avg Speed = Total Distance / Total Time

Instanteous Speed vs Average Speed Traffic police catching speeding vehicles: are they interested in instantaneous speed or average speed? How do they measure this? The toll booth in the Malaysian highway charges you for speeding if you take too short a time to travel from place A to place B. Are they measuring instantaneous speed or average speed? How can you avoid being charged?

Task 1: GLM pg 30, Qn 3(a)-(c) Task 2: GLM pg 31, Qn 4 (a)-(b)

Distance vs Displacement If I walked 3 metres to the front and then 6 metres to the back: How far have I travelled? This is an ambigious question. There are two ways of interpreting this question: 1) How much total distance have I travelled? 2) How much distance is there between my current position and my starting position? The first is asking for the quantity “distance” The second is asking for the quantity “displacement”

Displacement Symbol for displacement is “s” Units: m Question: is it possible to have negative displacement? How about distance? Direction matters for displacment, but doesn’t matter for distance! Note: in this topic we are generally concerned about motion in a straight line (one-dimensional motion)

Speed vs Velocity You may have come across the term “velocity” and you may have used it interchangeably with “speed” In Physics they are actually different (but related) quantities The difference between speed and velocity is the same difference between distance and displacement

Speed vs Velocity Direction matters for velocity but does not matter for speed The sign convention for velocity follows the sign convention for displacement E.g. if moving to the right is positive displacement, moving to the right is positive velocity as well

Speed vs Velocity Official definition (to be memorized) Speed is the distance moved per unit time Velocity is the rate of change of displacement

Scalars vs Vectors Quantities which have direction as well as magnitude are known as vectors Quantities which only have magnitude are known as scalars This is the list of scalars and vectors which you have studied so far: ScalarsVectors MassForce (e.g. Weight) DistanceDisplacement SpeedVelocity

Acceleration In English, we use the term “acceleration” to describe an object which is going faster and faster (as opposed to constant speed) If an object is going slower and slower, does it have acceleration? Yes!! As long as an object has changing velocity, it has an acceleration Definition: the rate of change of velocity

Practice Task Task 1: GLM pg 30 Qn 2(a)-(e) Task 2: GLM pg 31 Qn 4 (c)

Acceleration Question: A car is making a right turn at constant speed. Does it have an acceleration? Yes! The direction of the car changed, hence the velocity of the car changed (recall that velocity is a vector). Thus there is a acceleration.

Acceleration Question: the moon is orbiting around the Earth at constant speed. Does it have an acceleration? Yes! The direction of the velocity of the moon is constantly changing, hence the velocity of the moon is constantly changing, hence there is an acceleration!

Uniform Acceleration (straight line) When an object is changing its velocity at a constant rate, it is said to have uniform acceleration Definition: a constant rate of change of velocity

Uniform Acceleration The following equation applies (only) if acceleration is uniform: a = (v-u)/t – a = acceleration – u = initial velocity – v = final velocity – t = time From this equation, can you determine units of acceleration?

Deceleration You may come across the term “deceleration”, referring to an object going slower and slower. Deceleration is actually negative acceleration Uniform deceleration is when an object is going slower and slower at a constant rate. In uniform deceleration cases, you may still use the equation a = (v-u)/t, but acceleration must be a negative value

Practice Task Task 1: GLM pg 33 Qn 2 Task 2: GLM pg 33 Qn 3, find the final speed of the boy instead of time taken to finish the race

Important! Presentation of Working in Calculation Questions Step 1: Equation Step Step 2: Substitution Step Step 3: Intermediate Answers calculate to at least 4 s.f. Step 4: Final Answers provide to 3 s.f, with correct units

Quiz 2A

Assignment 2A TYS Topic 2 Paper 1: Qn 1, 3, 5, 8, 12 Due Date: Reminder: Late Work Policy

Kinematics Graphs Often in kinematics, we use graphs to describe the motion of objects, since graphs can provide a lot of information while taking less space You need to be familiar two kinds of graphs: 1) Displacement – Time Graphs 2) Velocity – Time Graphs

Displacement-Time Graph In an s-t graph, the vertical axis represents displacement (s) while the horizontal axis represents time (t) Reading an s-t graph helps us to find a) the displacement of an object at any one time b) the velocity of an object at any one time

s-t graph (uniform velocity) Can you describe the graph below? What is the velocity when t = 10 s? s/m t/s 2 4 6 8 10 12 100 60 40 20 0 80

Characteristics of s-t graph (uniform velocity) Straight line gradient is the same at any point on the straight line the gradient represents velocity What is happening if the s-t graph shows a flat line? What is happening if the s-t graph shows a line which is sloping downwards?

s-t graph (non-uniform velocity) Can you describe the velocity of this object? gradient is increasing = velocity is increasing s/m t/s 2 4 6 8 10 12 14 16 18 20 100 80 60 40 20 0

s-t graph (non-uniform velocity) Can you describe the velocity of this object? gradient is decreasing = velocity is decreasing s/m t/s 2 4 6 8 10 12 14 16 18 20 100 80 60 40 20 0

Characteristics of s-t graph (non- uniform velocity) curve Find gradient by taking the tangent of the curve gradient represents instantaneous velocity gradient changing with time = velocity changing with time increasing gradient = increasing velocity decreasing gradient = decreasing velocity

Quiz 2B

Assignment 2B TYS Topic 2 Paper 2 Qn 1 [handout]

Velocity-Time Graph In a v-t graph, the vertical axis represents velocity while the horizontal axis represents time Reading a v-t graph can help us to find: 1) instantaneous velocity at any one point in time 2) instantaneous acceleration at any one point in time 3) displacement covered in a time interval (between two points in time)

v-t graph (uniform acceleration) Gradient of v-t graph = acceleration What is the acceleration of this object?

Characteristics of v-t graph (uniform acceleration) Straight line graph Gradient is constant = acceleration is constant What would a v-t graph of an object with constant velocity look like? What would a v-t graph of an object at rest look like? What would a v-t graph of an object with uniform decreasing velocity look like?

v-t Graph (non-uniform acceleration) Can you describe this graph? gradient is decreasing = acceleration is decreasing 1 2 3 4 5 6 7 8 9 10 11 12 v/m s -1 t/s 0 20 10 30

Characteristics of v-t graph (non- uniform acceleration) curve gradient represents instantaneous acceleration gradient changing with time = acceleration changing with time increasing gradient = increasing acceleration decreasing gradient = decreasing acceleration

finding displacement from v-t graphs Unlike s-t graphs, there is one more way to gain information from v-t graphs (aside from finding gradient) The area under a time interval v-t graph shows the displacement covered by that time interval

finding displacement from v-t graphs Find displacement covered: a) t = 0 s to t = 3 s b) t = 3 s to t = 7.5 s c) t = 7.5 s to t = 12 s d) in total? t/s v/m s -1 0 1 2 3 4 5 6 7 8 9 10 11 12 10 20 30 40 50

Drawing your own v-t graph Sometimes a graph may not be provided, but you may be required to sketch your own v-t graph to solve the question.

Practice Task Task 1: GLM pg 42, Qn 1, 3 Task 2: GLM pg 33, Qn 3 (actual question)

Quiz 2C

Putting it all together Most numerical problems involve 4 of these 5 quantities: v, u, a, s, t auvtsauvts If question involves these 4 quantities, use a = (v-u)/t to solve If question involves these 4 quantities, draw your own v-t graph to solve

Putting it all together s-t graphv-t graph read off the graph displacementvelocity gradientvelocityacceleration area under-displacement

Putting it all together Velocity Acceleration Displacement gradient (differentiate) area under (integrate)

Assignment 2C TYS Topic 2 Paper 1: Qn 5, 7, 9 Paper 2: Qn 4, 6

Summary instantaneous vs average speed scalars vs vectors a = (v-u)/t s-t graphs – finding velocity v-t graphs – finding acceleration – finding displacement – drawing own v-t graph

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