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Physics 211 Lecture 3 Speed, Velocity, and

Acceleration

Some Definitions

- Kinematics the study of motion
- Translational motion movement from one point to

another - Rotational motion movement of a body around an

axis passing through it - Vibrational motion movement which is a

repetitive, back and forth, motion between the

same two points - Point or particle model for mass Objects (even

large ones) can be treated like infinitesimally

small particles moving as a point. This point is

the center of mass of the object.

A Few Words about Motion

- Simplest motion - occurs when an object moves at

constant speed in one dimension. - One-dimensional motion in this course

x-direction, thus we have - x position of a particle on the x-axis

(location) - x x(t) position of a particle as a function

of time (motion) - Real-world motion is usually 2D or 3D, but

simplifications to 1D or 2D are commonly

sufficient in solving motion problems.

One Dimensional Motion

Instantaneous velocity (velocity) derivative of

displacement with respect to time (vector)

Distance summation of total length of movement

along a path of motion

Displacement net change in position of a

particle (vector)

Instantaneous speed magnitude of velocity

(scalar)

Average Speed total distance traveled by a

particle divided by time interval over which

travel occurred (scalar)

Average acceleration change in velocity of a

particle divided by time interval over which

velocity change occurred (vector)

Average velocity displacement of a particle

divided by time interval over which displacement

occurred (vector)

Instantaneous speed derivative of velocity with

respect to time (vector)

Graphs of Position, Velocity, and Acceleration

vs. Time

x

t

v

t

a

t

Example Straight Line Motion in 1D with Constant

VelocityAn object traveling at a constant

velocity of 2 m/s is measured at a position of 3

m at time zero on an air track. Find the

equation of motion (x position as a function of

time) for this line and display it graphically.

Recall that dx/dtvo.

Example Damped Sinusoidal Oscillation w/ Varying

Pos/Vel/AccelA particular location on a guitar

string is vibrating above and below its normal

position with the following position as a

function of time Find the velocity and

acceleration of the string and display it

graphically.

Questions for Groups

- 2.2 The avg. velocity of a particle moving in 1D

is positive. - Could the instantaneous velocity have been

negative during the interval? - Suppose the particle started at x0. Could the

particle even have been in the x region of the

axis? - 2.7 If the velocity of a particle is nonzero,

can its acceleration be zero? Explain. - 2.8 If the velocity of particle is zero, can its

acceleration be nonzero? Explain. - 2.10 Is it possible for the velocity and the

acceleration of an object to have opposite signs?

- If not, state a proof.
- If so, give an example of a situation and sketch

a velocity-time graph to show it.

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