Kinematics

Lesson Objectives

At the end of lesson, students should be able to:

State what is meant by distance and displacement. State what is meant by speed and velocity, and

calculate average speed and velocity. State what is meant by uniform acceleration, and

calculate acceleration..

Lesson Objectives

House

You are visiting a friend on his island. One day, he shows you a map of the island. At the bottom of the map there is this message. “Dig 3km away from the house for the treasure.” Both of you decide to set off to find this treasure.

Treasure Map

Path A:2km

Path E:3km

Path F:1.5km

Path D:1.5km

Path B:1km

Path J:3km

Path C:3km

Path H:1km

Path G: 3 km

Path I:2km

Treasure Map

Where do you start to dig for the treasure?

Is there enough information to know where to dig?

What other information do we need?

Recall

What is a vector? Let us look at this table below and fill in the

blanks.Physical Quantities Scalars or Vectors

Length  

Mass  

Weight  

Temperature  

Moment  

Scalar

Scalar

Scalar

Vector

Vector

Distance and Displacement

Distance

A scalar quantity

Magnitude only.

Displacement

A vector quantity

Magnitude and direction

Treasure Map

Path A:2km

Path E:3km

Path F:1.5km

Path D:1.5km

Path B:1km

Path J:3km

Path C:3km

Path H:1km

Path G: 3 km

Path I:2km

Where to dig?

We decide to dig at the hills for the treasure. We walk along path A and D from the house. The total distance we have traveled is 1.5km + 1.5km = 3km.

Where to dig?

Path D:1.5km

Path A:1.5km

450

Displacement Calculation

Let displacement be s

By Pythagoras Theorem

s2 = 1.52 + 1.52

s = (1.52 + 1.52)

s = 2.12km

s = 2.12km

However, our displacement is not 3 km. Our displacement is shown by the direct line (in red)

Where to dig?

Instead of walking to the hills, we decide to dig at the rock. We start from the house and then walk west for 3km to reach the rock and we dig there.

What is our distance traveled? Distance traveled = 3 km

What is our displacement? Displacement = 3km , west

Distance and displacement

Question 1Starting from the house,

We walk along path B, path G and path H. What is our (i) Distance traveled. (ii) Displacement.

(i) Distance traveled = 1+3+1 = 5km

(ii) Displacement = 3km, West

Distance and displacement

Question 2

Starting from the house,

We walk along path C, path I and path J. What is our (i) Distance traveled. (ii) Displacement.

(i) Distance traveled = 3+2+3 = 8km

(ii) Displacement = 2km, north

Distance and displacement

Question 3

Starting from the house,

We walk along path B. What is our

(i) Distance traveled. (ii) Displacement.

(i) Distance traveled = 1km

(ii) Displacement = 1km, south

Distance and displacement

Question 4Starting from the house,

We walk along path A, path D, path E, Path F, and path B. What is our

(i) Distance traveled. (ii) Displacement.

(i) Distance traveled = 2+1.5+3+1.5+1 = 9km

(ii) Displacement = 0Distance vs. Displacement applet

Practice Question 1

The diagram below shows position of a cross-country skier at

various times. The skier moves from A to B to C to D. Determine

the distance traveled by the skier and the resulting

displacement during these three minutes.

Distance Traveled = 180+140+100 = 420m

Total Displacement = 140m to the right

Practice Question 2

Diagram below shows several of Beckham’s positions at various

times of a football game. Beckham moves from position A to B to C

to D. What is Beckham's resulting displacement and distance

traveled?

Distance Traveled = 35+20+40 = 95m

Total Displacement = 55m to the left

SpeedDefinition: Speed is defined as the rate of change of distance with time.Equation: v = s / twhere v = speed; s = distance; t = time interval

Speed & Velocity

Example:A motorcycle covers a distance of 15 km in 30 minutes.Q. What is the motorcycle’s average speed?  Q. Does the average speed help us to determine the maximum or minimum speed of the motorcycle?  Q. The above answer seems slow for a motorcycle. Explain why it is probably correct.

<v> = s / t = 15 km / (30/60) h = 15 km / 0.5 h = 30 km h-1

No, it does not.

Average speed is just an average value for the car. For example, on an Expressway, the motorcycle could be travelling at 80km/h. After exiting from Expressway, the motorcycle gets stuck in a traffic jam and travels at 5 km/h. As such, it could be travelling faster at times and slower at other times whichis why the average speed seems correct.

Speed & Velocity

Question 1:A plane travels at a constant speed and covers a distance of 2750 km in a period of 2 hours 30 minutes. What is the speed of the aeroplane?

s = 2750 km

t = 2 h 30 min = 2.5 h

<v> = s / t = 2750 km / 2.5 h = 1100 km/h

Speed & Velocity

Question 2:A man walks along his garden path in 2 mins. If his average speed for the walk was 2 m/s, how long is his garden path?

t = 2 mins = 120s

<v> = 2 m/s

s = <v> x t = (2 x 120) m = 240m

Note the SI units of speed and time in this example.

Speed & Velocity

Question 3:A man jogs a distance of 8 km in 40 minutes. Calculate his average speed in (i) km/h & (ii) m/s.

(i) <v> = s / t = 8km / (40/60)h = 12 km/h

(ii) <v> = s / t = (8 x 1000)m / (40 x 60)s = 3.33 m/s

Speed & Velocity

Question 4:Convert the following speeds between m/s and km/h.i) 15 m/s & ii) 100 km/h

(i) v = 15 m/s = (15/1000)km / (1/60x60)h = 54 km/h

(ii) v = 100 km/h = (100 x 1000)m / (1 x 3600)s = 27.8 m/s

Speed & Velocity

Question 5:You walk a distance of 2 km at an average speed of 8 km/h. You then run for a further 5 minutes with an average speed of 14 km/h. What is your average velocity for the whole journey?

s1 = 2 kmv1 = 8 km/ht1 = s1 / v1 = 2/8 h = ¼ h

v2 = 14 km/ht2 = 5 min = 5/12 hs2 = v2 x t2 = 14 km/h x 5/12 h = 35/6km

<v> = (s1 + s2) / (t1 + t2) = (35/6 + 2)km / (1/4 + 5/12)h<v> = 11.75 km/h

Speed & Velocity

VelocityVelocity is a vector and has both magnitude and direction..

Definition:Velocity is defined as the rate of change of distance in a specified direction with time.

Velocity can also be defined as the rate of change of displacement with time.

Speed & Velocity

Example:A car drives 40 km north along a road and then 20km south along the same road. It takes 2 hours to complete its journey. Calculate:a) average speed for the journey ; b) the average velocity for the journey.a) Total Distance = 40 + 20 km = 60 km

Time = 2hAverage speed = distance / time = 60 km / 2h = 30 km/h

b) Displacement = (40 –20) km = 20 kmTime = 2hAverage velocity = displacement / time = 20/2

= 10 km/h (towards north).

Speed & Velocity

 

Acceleration is defined as the rate of change of velocity with respect to time.

Equation:

a = (v – u) t where a = acceleration in m s-2 ; v = final velocity in m s-1 ; u = initial velocity in m s-1 ; t = time interval between the change from the initial velocity to the final velocity.

Acceleration

 

Example 1:A bus at rest is accelerated to a velocity of 30 m/s in 10 seconds. Calculate the acceleration of the bus.

Solution:Initial velocity, u = 0 m s-1.Final velocity = v = 30 m s-1.Time interval = t = 10 s.

a = (v – u) / t = [(30 – 0) / 10] m s-2 = 3 m s-2.

Acceleration

 

Question 1:A car is travelling at a constant velocity of 20 m/s before it accelerates to a velocity of 65 m/s in 5 seconds. What is the acceleration of the car?

Solution:u = 20 m s-1.v = 65 m s-1.t = 5 s.

a = (v – u) / t = [(65 – 20) / 5] m s-2 = 9 m s-2.

Acceleration

 

Question 2:A car initially has a velocity of 60 m/s. After braking for 5 seconds it has a velocity of 20 m/s. Calculate the acceleration of the car.

Solution:u = 60 m s-1.v = 20 m s-1.t = 5 s.

a = (v – u) / t = [(20 – 60) / 5] m s-2 = - 8 m s-2.

Note the negative sign for the acceleration in this case.

Acceleration

 

Deceleration When an object reduces its velocity (or speed),we can state this in several way. We can say that the object (a) is experiencing deceleration ;

(b) is experiencing retardation ;

(c) is experiencing negative acceleration.

Acceleration

 

Question 3: A train slows down from 80 m/s to rest in one minute. Calculate the retardation of the train.

Solution:u = 80 m/s ;v = 0 m/s ;t = 1min = 60 s ;a = (v-u) / t = [(0 – 80) / 60] m/s2 = - 1.33 m/s2

Since acceleration is – 1.33 m/s2 , retardation is 1 m/s2 .

Acceleration

Concept Map

Write down one thing you have learnt in this lesson.

Displacement

Velocity

Acceleration

Is the rate of change of displacement per unit time

Is the rate of change of velocity per unit time

v = s t

a = (v – u) t

All these quantities are

Vectors.

They have both magnitude and

direction .