Phys 270- 2: Motion Along A Straight Line

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Physics with mechanics:

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the study of the relationships among force, matter, and motion

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kinematics:

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the part of mechanics that enables us to describe motion

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dynamics:

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relates motion to its causes

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Displacement:

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a vector points along from P1 to P2

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the x-component of the displacement:

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the change in the value of x, that took place during the time interval.

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average velocity:

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a vector quantity whose x-component is the change in x divided by the time interval

ex: m/s

- depends on the particular time interval chosen.

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average x-velocity:

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the x-component of displacement, divided by the time interval during which the displacement occurs

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2.1 positions of a dragster at two times during its run.

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simple rules for the average x-velocity:

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- whenever x is positive & increasing or is negative and becoming less negative, the particle is moving in the + x-direction and avg. velocity is positive.

- whenever x is positive and decreasing or is negative and becoming more negative, the particle is moving in the - x-direction and avg. velocity is negative.

(if a particle moves in the negative x-direction during a time interval, its avg. velocity for that time interval is neg. )

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2.3 The position of a dragster as a function of time:

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Instantaneous velocity:

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tells us how fast / in what direction the particle was moving at any given time during the interval.

velocity at any specific instant of time or specific point along the path.

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The instantaneous velocity:

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- the limit of the average velocity as the time interval approaches 0.

- the instantaneous rate of change of position with time.

Vx = instantaneous velocity

+ value: x is increasing and the motion is in the positive x-direction

- value: x is decreasing and the motion is in the negative x-direction.

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Speed:

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the distance traveled divided by time.

V = instantaneous speed

it measures how fast and in what direction object is moving.

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Scalar:

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a simple physical quantity that is not changed by coordinate system rotations or translations...

no info. about direction.

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Motion diagram:

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shows the particle's position at various times as well as arrows to represent the particles velocity at each instant.

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Average acceleration:

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as it moves from P1 to P2 to be a vector quantity whose x-component
a av-x (average x-acceleration) equals the change in the x-component velocity divided by the time interval of the change in time.

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Velocity:

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describes how a body's position changes with time.

- tells us how fast and in what direction the body moves

= dx/dt (the derivative of the position with respect to time)

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acceleration:

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describes how the velocity changes with time.

- it tells us how the speed and direction of motion are changing.

= dv/dt (the derivative of velocity with respect to time)

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The instantaneous acceleration:

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the limit of the average acceleration as the time interval approaches 0.

- equals the instantaneous rate of change of velocity with time.

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2.12: a graph of motion:

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Velocity of x at constant acceleration:

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Final position formula using its initial position, initial velocity, acceleration (at constant x-acceleration)

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Equations of motion with constant acceleration:

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Problem-solving strategy 2.1: Motion with Constant Acceleration:

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Free Fall:

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the motion of a falling object that is influenced by and only by gravity:

- includes rising as well as falling motion.

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Acceleration due to gravity:

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the constant acceleration of a freely falling body:

- denote its magnitude with (g)

g = 9.8m/ sq. sec.
g= 980cm/sq.sec.
g= 32ft/sq. sec.

note: since g is the magnitude of a vector quantity, it is always a positive number

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How can we find the position and velocity from the acceleration function Ax(t)?

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Velocity with varying acceleration:

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Position with varying acceleration:

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Chapter 2 summary:

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