chapter 2 kinematics everything in the universe is in motion. nothing is permanently at rest....

Chapter 2

Chapter 2

Kinematics

Kinematics

Everything in the universe is in motion. Nothing is permanently at rest.

Everything in the universe is in motion. Nothing is permanently at rest.

These slides adapted from materials from Longman~ Ismail Brian Wee, 2009 ~ Slide 1 of 24

ContentsContents

Speed, Velocity and Acceleration

Graphical Analysis of Motion

Free-fall

Chapter Review


Graphical Analysis of Motion

Free-fall

Chapter Review

Slide 2 of 24

Speed of an object is defined as the Speed of an object is defined as the distance travelled per distance travelled per unit timeunit time..Speed of an object is defined as the Speed of an object is defined as the distance travelled per distance travelled per unit timeunit time..

Speed, vSpeed, v

SpeedSpeed

SI unit of metres per second (ms-1) SI unit of metres per second (ms-1)

speed (ms-1) = speed (ms-1) = time taken (s)

distance travelled (m)

* Note: Remember to USE THE CORRECT UNITSSlide 3 of 24

Average speed of an object is defined as the Average speed of an object is defined as the total distance total distance travelled divided by the total time takentravelled divided by the total time taken..Average speed of an object is defined as the Average speed of an object is defined as the total distance total distance travelled divided by the total time takentravelled divided by the total time taken..

Average Speed, vAverage Speed, v

SpeedSpeed

has a unit of metres per second (ms-1) has a unit of metres per second (ms-1)

for most journeys, speed is not constant for most journeys, speed is not constant

average speed (ms-1) = average speed (ms-1) = total time (s)

total distance (m)

* Note: Remember to USE THE CORRECT UNITS

Slide 4 of 24

A speedometer measures the A speedometer measures the instantaneous speed of the carinstantaneous speed of the car

Instantaneous SpeedInstantaneous Speed

SpeedSpeed

Instantaneous speed is the speed of an object at any instant (any point in time).Instantaneous speed is the speed of an object at any instant (any point in time).

Slide 5 of 24

Velocity is the Velocity is the displacement per unit timedisplacement per unit time in a stated in a stated direction; or speed in a specified direction.direction; or speed in a specified direction.Velocity is the Velocity is the displacement per unit timedisplacement per unit time in a stated in a stated direction; or speed in a specified direction.direction; or speed in a specified direction.

Velocity, vVelocity, v



has a unit of metres per second (ms-1) has a unit of metres per second (ms-1)

Velocity (ms-1) = Velocity (ms-1) = time (s)

displacement (m)


Slide 6 of 24

A negative velocity indicates that a body is moving in the A negative velocity indicates that a body is moving in the opposite direction to the direction stated.opposite direction to the direction stated.A negative velocity indicates that a body is moving in the A negative velocity indicates that a body is moving in the opposite direction to the direction stated.opposite direction to the direction stated.

Speed Speed Velocity Velocity

scalar quantity vector quantity

regardless of its direction

dependent on direction of motion

Difference between Speed & VelocityDifference between Speed & Velocity

Speed and VelocitySpeed and Velocity

Slide 7 of 24

Consider a vehicle travelling around a bend.Consider a vehicle travelling around a bend.Consider a vehicle travelling around a bend.Consider a vehicle travelling around a bend.

VelocityVelocity

VelocityVelocity

At a road bend, although the vehicle’s speed is constant, its velocity is continuously changing (because direction is constantly changing)

At a road bend, although the vehicle’s speed is constant, its velocity is continuously changing (because direction is constantly changing)

Slide 8 of 24

Acceleration (ms-2) = Acceleration (ms-2) = time taken for the change (s)

change of velocity (ms-1)

Acceleration is defined as the Acceleration is defined as the rate of change of velocityrate of change of velocity..Acceleration is defined as the Acceleration is defined as the rate of change of velocityrate of change of velocity..

AccelerationAcceleration


has a unit of metres per second square (ms-2) has a unit of metres per second square (ms-2)


a = a = t

v – u this formula is often used,

where

v Final Velocity (ms-1)

u Initial Velocity (ms-1)

t Time taken (s)

this formula is often used, where

v Final Velocity (ms-1)

u Initial Velocity (ms-1)

t Time taken (s)Slide 9 of 24

UniformUniform acceleration occurs when the velocity increases acceleration occurs when the velocity increases (or decreases) by the same amount per unit time. (or decreases) by the same amount per unit time. [Or rate of change of velocity is constant/uniform][Or rate of change of velocity is constant/uniform]

UniformUniform acceleration occurs when the velocity increases acceleration occurs when the velocity increases (or decreases) by the same amount per unit time. (or decreases) by the same amount per unit time. [Or rate of change of velocity is constant/uniform][Or rate of change of velocity is constant/uniform]

No accelerationNo acceleration(acceleration = 0)(acceleration = 0)

Accelerating Accelerating (positive (positive

acceleration)acceleration)

Decelerating Decelerating (negative (negative

acceleration)acceleration)

velocity of the moving object is

constant throughout

velocity is increasing

velocity is decreasing



Slide 10 of 24

Graphical analysis of motionGraphical analysis of motion

Distance is the actual or total length travelled by an object in motion.Distance is the actual or total length travelled by an object in motion.

DistanceDistance

Displacement is the distance measured along a straight line in a stated direction.Displacement is the distance measured along a straight line in a stated direction.

DisplacementDisplacement

A BDisplacement

Distance

Slide 11 of 24


Displacement-time graphsDisplacement-time graphs

Gradient Gradient of the displacement-time graph gives the of the displacement-time graph gives the velocityvelocity of the object.of the object.Gradient Gradient of the displacement-time graph gives the of the displacement-time graph gives the velocityvelocity of the object.of the object.

Displacement / m

Time / s

Displacement / m

Time / s

object is not moving

faster

slower

Slide 12 of 24


The displacement-time graph of an object travelling with The displacement-time graph of an object travelling with constant velocity is always a straight lineconstant velocity is always a straight line..The displacement-time graph of an object travelling with The displacement-time graph of an object travelling with constant velocity is always a straight lineconstant velocity is always a straight line..


object is moving with constant velocity

Displacement / m

Time / s

faster

slower

In a displacement-time graph, In a displacement-time graph, the GRADIENT shows the the GRADIENT shows the VELOCITY.VELOCITY.

Thus,Thus,

Steeper gradient Steeper gradient Higher Velocity (faster)Higher Velocity (faster)

Shallower gradient Shallower gradient Lower Velocity (slower)Lower Velocity (slower)

In a displacement-time graph, In a displacement-time graph, the GRADIENT shows the the GRADIENT shows the VELOCITY.VELOCITY.

Thus,Thus,

Steeper gradient Steeper gradient Higher Velocity (faster)Higher Velocity (faster)

Shallower gradient Shallower gradient Lower Velocity (slower)Lower Velocity (slower)

Slide 13 of 24


Displacement-time graphsDisplacement-time graphsDisplacement-time graphsDisplacement-time graphs

Time taken, t/s 0 10 20 30 40 50 60 70

Distance, x/m 0 50 100 200 350 550 850 1200

The The instantaneous instantaneous speedspeed of the car at of the car at a particular time a particular time can be obtained by can be obtained by finding the finding the slope of slope of the tangent to the the tangent to the graph (gradient) at graph (gradient) at that point in timethat point in time..

The The instantaneous instantaneous speedspeed of the car at of the car at a particular time a particular time can be obtained by can be obtained by finding the finding the slope of slope of the tangent to the the tangent to the graph (gradient) at graph (gradient) at that point in timethat point in time..

In each successive time interval, 0-10 s, 10-20 s, and so on, the car covers a greater distance than in the previous one. This means the car is going faster.

550550

Slide 14 of 24


Gradient of a tangent to the displacement-time graph of Gradient of a tangent to the displacement-time graph of an object travelling with non-uniform velocity gives its an object travelling with non-uniform velocity gives its instantaneous velocity at a given time.instantaneous velocity at a given time.

Gradient of a tangent to the displacement-time graph of Gradient of a tangent to the displacement-time graph of an object travelling with non-uniform velocity gives its an object travelling with non-uniform velocity gives its instantaneous velocity at a given time.instantaneous velocity at a given time.

Time / sTime / s

increasing velocity

decreasing velocity

Displacement / m Displacement / m


object has variable velocity

Slide 15 of 24


Velocity-time graphsVelocity-time graphs

Gradient of the velocity-time graph gives the acceleration Gradient of the velocity-time graph gives the acceleration of a moving body.of a moving body.Gradient of the velocity-time graph gives the acceleration Gradient of the velocity-time graph gives the acceleration of a moving body.of a moving body.

Velocity / ms-1

Time / s Time / s

Velocity / ms-1

object is not moving

object moves with constant velocity

Slide 16 of 24


Velocity-time graphsVelocity-time graphs

GradientGradient of the velocity-time graph gives the of the velocity-time graph gives the accelerationacceleration of a moving body.of a moving body.GradientGradient of the velocity-time graph gives the of the velocity-time graph gives the accelerationacceleration of a moving body.of a moving body.

Time / sTime / s

acceleration deceleration

Velocity / ms-1 Velocity / ms-1

object has constant acceleration object has constant deceleration

Slide 17 of 24


Time / sTime / s

Velocity / ms-1 Velocity / ms-1

Variable accelerationVariable acceleration

Gradient of the velocity-time graph gives the acceleration Gradient of the velocity-time graph gives the acceleration of a moving body.of a moving body.Gradient of the velocity-time graph gives the acceleration Gradient of the velocity-time graph gives the acceleration of a moving body.of a moving body.

object has variable acceleration/deceleration

increasing acceleration

decreasing acceleration

Slide 18 of 24


Not all objects move with constant acceleration. Most Not all objects move with constant acceleration. Most vehicles move with accelerations that keep changing.vehicles move with accelerations that keep changing.

The acceleration or deceleration of the object at any point in The acceleration or deceleration of the object at any point in time is still given by the gradient of the graph at that point.time is still given by the gradient of the graph at that point.

Not all objects move with constant acceleration. Most Not all objects move with constant acceleration. Most vehicles move with accelerations that keep changing.vehicles move with accelerations that keep changing.

The acceleration or deceleration of the object at any point in The acceleration or deceleration of the object at any point in time is still given by the gradient of the graph at that point.time is still given by the gradient of the graph at that point.

Variable accelerationVariable acceleration

velocity-time graph of a car on a straight road where it has to stop twice because of traffic lights

time/s

velocity/m s-1

stopstop

Slide 19 of 24

graphical analysis of motiongraphical analysis of motion

area under a velocity-time grapharea under a velocity-time graph

The area under the velocity-time graph gives the distance travelled by the moving object.The area under the velocity-time graph gives the distance travelled by the moving object.

Velocity / ms-1

Time / st1

v

Distance travelled = area under graph (use square formula)

= v t1

Distance travelled = area under graph (use square formula)

= v t1

uniform velocity

In this example,

Slide 20 of 24


Area under a velocity-time graphArea under a velocity-time graph

The area under the velocity-time graph gives the distance travelled by the moving object.The area under the velocity-time graph gives the distance travelled by the moving object.

Velocity / ms-1

Time / s

v

t1

uniform

accelera

tion

Distance travelled = area under graph (use triangle formula)

= ½ v t1

Distance travelled = area under graph (use triangle formula)

= ½ v t1

In this example,

Slide 21 of 24


Area under a velocity-time graphArea under a velocity-time graph

The The areaarea under the velocity-time graph gives the under the velocity-time graph gives the distancedistance travelled by the moving object.travelled by the moving object.The The areaarea under the velocity-time graph gives the under the velocity-time graph gives the distancedistance travelled by the moving object.travelled by the moving object.

uniform deceleration

uniform velocity

Area of trapezium = ½ x (a + b) x height

Velocity / ms-1

Time / st2

v

t1

Distance travelled = area under graph (use trapezium formula)

= ½ ( t1 + t2) v

Distance travelled = area under graph (use trapezium formula)

= ½ ( t1 + t2) v

In this example,

* Note: You can also find the area by adding the area of the square and the area of the triangle

Slide 22 of 24

Free fallFree fall

Acceleration due to gravityAcceleration due to gravity

All objects fall freely towards the centre of the earth and have the same acceleration (acceleration of free fall).All objects fall freely towards the centre of the earth and have the same acceleration (acceleration of free fall).

all objects fall freely at g 10 ms-2 ( if air resistance is negligible )

speed of a free-falling body increases by 10 ms-1 every second or when a body is thrown up

speed of a free-falling body decreases by 10 ms-1 every second or when a body is thrown up

all objects fall freely at g 10 ms-2 ( if air resistance is negligible )

speed of a free-falling body increases by 10 ms-1 every second or when a body is thrown up

speed of a free-falling body decreases by 10 ms-1 every second or when a body is thrown up

Slide 23 of 24

DistanceDistanceDisplacementDisplacement

Velocity-Velocity-time graphtime graph

is used to find

is used to find

can be plotted as

represents

represents

provides

provides

acceleration =acceleration =change in velocitychange in velocity

timetime

Gradient of Gradient of velocity-velocity-

time graphtime graph

Area under Area under velocity-velocity-


average speed =average speed =total distancetotal distance

total timetotal time

distancedistance

timetimespeed =speed =

displacementdisplacement

timetimevelocity =velocity =

Gradient of Gradient of displacement-displacement-


represents

Displacement-Displacement-time graphtime graph

gives

can be plotted as

Slide 24 of 24

chapter 2 kinematics everything in the universe is in motion. nothing is permanently at rest....

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