Speed and velocity

Learning objectives

Students will be able to

• Define speed

• Define velocity

• Calculate speed and velocity

WARM UP

Speed

• Distance moved per second or rate of change of distance

• It is scalar quantity

• Unit-m/s

• Average speed=Distance travelled/time taken

Velocity

• Velocity measures rate of change of displacement

• Average velocity=Displacement/time taken

• It is a vector quantity.

• Unit- m/s

CONTINOUS ASSESSMENT

1.What does the speedometer of a car measure?

2.A car travels a distance of 2oom and returns to the original position after 5min.What is the speed and velocity of the car?

3.What is the eqn. for speed?

4.What is the eqn. for time taken?

Final assessment

1.a)Define speedb) Define velocity

(page42)

HOME WORK

• Page.33

Example.2

GRAPHS

Displacement –time graph

a) Body at rest

t

S

t(s) 0 1 2 3 4

S(m) 2 2 2 2 2

b)Body moving with steady velocity

Gradient=

Gradient of displacement –time graph gives velocity. Steeper the line ,larger the velocity.

t

s

t(s) 0 1 2 3 4

S(m) 0 5 10 15 20

Time

ntDisplaceme

c)Accelerating body

a=2m/s²

Gradient at different time instants are different, as the velocity is changing at every instant.

Gradient at any instant gives the instantaneous velocity

t

st 0 1s 2s 3s 4s

s 0m 1m 4m 9m 16

d)Decelerating body

t

s

Velocity –time graph

a) Body moving with steady velocity

t

v

b)Body moving with steady acceleration

• Gradient=

• Gradient of velocity –time graph gives acceleration.

• Steeper the line ,larger the acceleration.

t

v

t(s) 0 1 2 3 4

v(m/s) 0 5 10 15 20

onacceleratiTime

locityChangeinve

c)Body moving with steady deceleration

• Gradient=

• Gradient of velocity –time graph gives acceleration.

• Steeper the line ,larger the deceleration.

t

v

t(s) 0 1 2 3 4

v(m/s) 20 15 10 5 0

ondecelerationacceleratiTime

locityChangeinve/

Area under the velocity –Time graph gives the displacement

Calculate the total displacement of the given body using the given velocity time graph.

OA-accelerated motion; Displacement = 100m

AB-Steady velocity ; Displacement = 400m

BC—decelerated motion; Displacement = 50m

Total displacement = 100+400+50=550m

Page43. Qn . 8

a) acceleration= gradient of OA

=change on y/change on x

=y2-y1/X2-X1 =2-0/3-0

=2/3 =1.5m/s²

b) Decelerates, its velocity becomes zero and it reaches the maximum height.

c)At point C the velocity of the lift is zero. The height=Displacement=area under OABC

= ½ × 3 × 2 + 6 × 2 + ½ × 3 × 2

=3+12+3=18m.

d)The lift starts moving down. First it accelerates in the downward direction.Then it starts decelerating and come to rest e) 18-6=12m

PAGE 106

• Home Work

• Page 106 Qn.no.25a

Horizontally Launched Projectiles

Imagine a cannonball being launched from a cannon atop a very high cliff. What will be the path of the cannonball and how can the motion of the cannonball be described?

PROJECTILE• A projectile is an object upon which the

only force is gravity.

• Gravity, being a downward force, causes a projectile to accelerate in the downward direction.

• The force of gravity could never alter the horizontal velocity of an object .A vertical force does not effect a horizontal motion.

COMPONENTS OF A VECTOR

• These two parts of the two-dimensional vector are referred to as components.

• A component describes the effect of a single vector in a given direction. Any force vector that is exerted at an angle to the horizontal can be considered as having two parts or components.

• The vector sum of these two components is always equal to the force at the given angle. This is depicted in the diagram below.

ASinA

ACosA

y

x

COMPONENTS OF VECTORS

xA

A x

http://www.physicsclassroom.com/Class/vectors/u3l2a.cfm