KINEMATICS. DISTANCE AND DISPLACEMENT - DEFINITIONS DISTANCE is a numerical (scalar) description of how far apart objects are. – Distance is length of.

KINEMATICS

DISTANCE AND DISPLACEMENT - DEFINITIONS

• DISTANCE is a numerical (scalar) description of how far apart objects are.– Distance is length of the path

• DISPLACEMENT is the distance moved in particular direction (vector quantity)

• Unit of both distance and displacement is the meter (m)

DISTANCE VS DISPLACEMENT

A

B

Distance s = 50 m

Displacements = 30 m

SPEED AND VELOCITY - DEFINITIONS

• SPEED is distance travelled per unit time

– Speed is scalar quantity• VELOCITY is displacement per unit time

– Velocity is vector quantity• Unit of both the speed and the velocity is the meter

per second (ms-1)

AVERAGE AND INSTANTANEOUS VELOCITY

• Usually the body cannot travel with constant velocity. If we describe – the whole displacement of body and– whole time the body travelled,

we can calculate AVERAGE VELOCITY of the body, • AVERAGE VELOCITY describes average displacement of the

body per unit time.• If we broke our trip into lots of small pieces, we can

consider each piece as the straight line travelled with constant velocity called INSTANTANEOUS VELOCITY.

• INSTANTANEOUS VELOCITY describes how fast the body going in that moment of time and in witch direction

VELOCITY IS RELATIVE

• One body moves with different velocity consider different bodies.

• It means, that velocity is relative to body we measure the velocity.

v’ = 15 ms-1

10 ms-1

u =10 ms-1

v= 0 ms-1

u´=?v’=15ms-1

10 ms-1 + 15 ms-1 = 25 ms-1 (to the right)

u

v

Obs I

Obs II

v = 15 ms-1

10 ms-1

u=10 m/s

v = 15 ms-1

u‘=?u

v

10 ms-1 - 15 ms-1 = -5 ms-1 (to the right)

RELATIVE VELOCITY

• If the velocities of bodies A and B are given as vA and vB, then

• the relative velocity of A with respect to B vArelB (also called the velocity of A relative to B) is

• and the velocity of B relative to A is

ACCELERATION• ACCELERATION is the rate of change of velocity

• a – acceleration, v – the velocity at the end; u – the velocity in the beginning, t – time of changing velocity from u to v.

• Acceleration is a vector quantity• The unit of acceleration is meter per second per

second (ms-1)s-1 or ms-2

• If the velocity of the body reduces in time, then the acceleration of the body called as deceleration

DISPLACEMENT AND ACCELERATION

• If body moves with constant acceleration we can calculate the velocity and displacement from equations:

SIGN OF DISPLACEMENT, VELOCITY AND ACCELERATION

• All these quantities are vectors and the signs of these quantities describe their direction

• A POSITIVE displacement means that body has moved RIGHT

• A POSITIVE velocity means that body is moving to the RIGHT

• A POSITIVE acceleration means that the body either– moving to the RIGHT and getting FASTER or– moving to the LEFT and getting SLOWER or

FREE FALL

• When body is allowed to fall freely, we say it is in free fall

• Bodies falling freely on the earth fall with acceleration of about g=9.81 ms-2

• The body falls because of gravity, it means that direction of the vector g is always vertically down

• To calculate displacement, velocity etc we can use the same equations, we described, but we free falls acceleration g instead acceleration a.

GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS

Describe how changes:

velocity: v=?acceleration: a=?

Line A

GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS

Line BDescribe how

changes:velocity: v=?

acceleration: a=?

GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS

Line CDescribe how

changes:velocity: v=?

acceleration: a=?

GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS

Line D

Describe how changes:

velocity: v=?acceleration: a=?

GRAPHICAL REPRESANTATION OF MOTION – VELOCITY-TIME GRAPHS

v=0 ; a=0

v=const>0 ; a=0

v= const<0 ; a=0

a=const>0; v - increasing

GRAPHICAL REPRESANTATION OF MOTION – ACCELERATION-TIME GRAPHS

A; B; C – a=0

a = const > 0

INSTANTANEOUS VELOCITY

To find instantaneous velocity of constantly accelerating body, we draw tangent to the curve and find the gradient of the tangent – it is the same as velocity.

Δt

Δs

AREA UNDER TIME-VELOCITY GRAPH

area = v x Δt gives the displacement

Δt

v

v = const > 0

AREA UNDER TIME-VELOCITY GRAPH

u Area1 = u x Δt

Δt

v

AREA UNDER ACCELERATION-VELOCITY GRAPH

area = a x Δt gives the change in velocity

Δt

a

a = const > 0