Kinematics

Motion Day 1

Frame of Reference The object or point from which movement is determined

A. Movement is relative to an object that appears stationary B. Earth is the most common frame of reference

Using clip from movie , Top_Secret_Train_Station_Gag.mp4

Scalar versus Vector

• Scalar - magnitude only (e.g. volume, mass, time)

• Vector - magnitude & direction (e.g. weight, velocity, acceleration)

Pictorial Representation

• An arrow represents a vector – Length = magnitude of vector– Direction = direction of vector

• This arrow could represent a vector of magnitude 10 point to the “right”

Speed is a Rate

• In this case, rate implies a time dependence. • Examples:

– The number of laps you swim per hour– The number of times you sneeze per day– The number of vacations taken per year

• So speed is defined as the rate of motion• With our definition of motion we have:

Speed = rate of change in position

Speed

• The average speed of an object is defined as the total distance traveled divided by the total time elapsed

– Speed is a scalar quantity

Average speed total distance

total time

Speed dt

Velocity

• The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed

– Velocity is a vector quantity

total displacementAverage velocity total time

dVt

Speed, cont

• Average speed is the total distance divided by the total time

• SI units are m/s

Velocity

• It takes time for an object to undergo a displacement

• The average velocity is rate at which the displacement occurs

• generally use a time interval, so let ti = 0

f i f iaverage

f i

d d d ddVt t t t

Velocity continued

• Direction will be the same as the direction of the displacement (time interval is always positive)+ or - is sufficient

• Units of velocity are m/s (SI)• Other units may be given in a problem, but

generally will need to be converted

Acceleration• Change in velocity divided by the

change in time

a Vt

Acceleration• Changing velocity (non-uniform) means an

acceleration is present• Acceleration is the rate of change of the

velocity

• Units are m/s2 (SI), cm/s2 (cgs), and ft/s2 (US Cust)

Average Acceleration

• Vector quantity• When the sign of the velocity and the

acceleration are the same (either positive or negative), then the speed is increasing

• When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

Kinematic Equations

• Used in situations with uniform acceleration

• Homework: Rearrange each equation to solve for the other variables

2 2

2

/

2

12

f i

f i

i

V d tV V at

V V ad

d V t at