Motion in 1 Dimension. v In the study of kinematics, we consider a moving object as a particle. A...

Motion in 1 Dimension


v

In the study of kinematics, we consider a moving object as a particle.

A particle is a point-like mass having infinitesimal size and a finite mass.

Motion in One Dimension (2048)

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x

Displacement


The displacement of a particle is defined as its change in position.

(m)

x = xf xi

= 5 m 0 m

= 5 m

Note: Motion to the right is positiveMotion in One Dimension (2048)

0 2 4 6246

x

Displacement



(m)

x = xf xi

= 6 m 5 m

= 11 m

Note: Motion to the left is negativeMotion in One Dimension (2048)

0 2 4 6246

x

Displacement



(m)

x = xf xi

= (1 m) (6 m)

= 5 m

Note: Motion to the right is positiveMotion in One Dimension (2048)


Average velocity

The average velocity of a particle is defined as xv

tx

vx

x

t

x1

x2

t1 t2

x

t

12

12ttxx

Velocity is represented by the slope on a

displacement-time graph



Average speed

The average speed of a particle is defined as

time totaldistance total

speed Average



Instantaneous velocity

The instantaneous velocity v, equals the limiting value of the ratio

t

xv lim

0tx

dx

dt

x

t

dtdx

Instantaneous velocity is represented by

the slope of a displacement-time graph



Instantaneous speed

The instantaneous speed of a particle is defined as the magnitude of its instantaneous velocity.



Average acceleration

The average acceleration of a particle is defined

as the change in velocity vx divided by the time

interval t during which that change occurred.

tv

a xx

12

12ttvv

v

t

v1

v2

t1 t2

v

tAcceleration is

represented by the slope on a

velocity-time graph



Instantaneous acceleration

The instantaneous acceleration equals the derivative of the velocity with respect to time

t

va lim

0tx dtdv

dv

dt

v

t

Instantaneous acceleration is represented by

the slope of a velocity-time graph


t

x

t

v

t

a

Displacement, velocity and acceleration graphs

The slope of a velocity-timegraph represents acceleration

tv

a

The slope of a displacement-timegraph represents velocity

tx

v

t

x

t

v

t

a

t

The area under an acceleration-timegraph represents change in velocity.

v

vta

The area under a velocity-timegraph represents displacement.

x

xtv


Definitions of velocity and acceleration

dtdv

a Instantaneous acceleration

dtdx

v Instantaneous velocity

tx

vAverage velocity

tv

aAverage acceleration


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Motion in 1 Dimension. v In the study of kinematics, we consider a moving object as a particle. A...

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