2. Motion in one dimension

2.1. Position, velocity, speed ; 2.2. Instantaneous velocity, instantaneous speed ; 2.4. Average and instantaneous acceleration ; 2.6. Kinematic equations

By motion in one direction we

understand the motion of an object moving along a straight line

The three types of motion are

translational, rotational, vibrational

By using the particle model we

describe a moving object as a particle when its size is negligible compared to the distances involved in the motion being studied

A particle is a

point like object, that is, an object that has mass but is of an infinitesimal size

A particle’s position (x) is

the location of the particle with respect to a chosen reference point which we consider to be the origin of a coordinate system

The motion of a particle is completely known if its position is known at all times

4 ways of representing motion

verbal, tabular, graphical, mathematical

The displacement (Δx) of an object is defined as

its change in position at some time interval

The formula for the displacement is

Δx = xf - xi where xf = final position and xi = initial position

Distance is

the length of a path followed by a particle

The average velocity (vavg) of a particle is defined as

the particle displacement divided by the time interval during which that displacement occurrs.

The average velocity formula is

vavg = Δx / Δt

The average speed of a particle is defined as

the total distance divided by the time interval needed to travel that distance

Average speed formula

vavg = d / Δt

When is the magnitude of the average velocity smaller than the average speed ?

Only when a particle moves in the +x direction and then reverses the direction of its motion (Δx < d)

The instantaneous velocity (V)

is equal to the slope of the tangent to the x-t graph at that instant / is equal to the limiting value of the ratio Δx/Δt as Δt approaches 0

The instantaneous speed is defined as

the magnitude of instantaneous velocity

The average acceleration of a particle is defined as

its change in velocity divided by the time interval during which this change occurs

Average acclereation formula

aavg = Δv / Δt

The instantaneous acceleration is

equal to the slope of the tangent to the v-t graph at that instant / equal to the limiting value of the ratio Δv/Δt as Δt approaches 0 / equal to the second derivative of x with respect to time

a=const gives us a=aavg

Position free kinematic equation

vf = vi + at

Acceleration free kinetic equation

xf = xi + ½ (vi+vf)t

Final velocity free kinematic equation

xf = xi + vit + ½ at²

Time free kinematic equation

vf² = vi² + 2a(xf-xi)

When a=0

vx=vavg=v , xf = xi + vt

A freely falling object is

any object moving freely under the influence of gravity alone, regardless of it’s initial motion

Freely falling objects experience an acc called

free fall acceleration or acceleration due to gravity (g)

Free fall acceleration’s value is

9.8 m/s²