KinematicsDescribing how things move is called kinematics and it has terms that are very specific. These terms include position, displacement, distance, velocity, speed and acceleration. Proper use of these terms first demands that you understand each term’s definition, symbol and any equations associated with it.

POSITION, DISPLACEMENTKinematics is a branch of physics that is concerned with describing motion. The first concept of motion is position. Think of your position at this instant. Another way of asking this question is “Where are you?”

Position is defined as the distance and direction from a reference point. A reference point may be in fact moving (e.g. Earth). Reference points are arbitrary choices made by us. Position is a vector quantity because it has size or magnitude and direction. Scalar quantities have only size or magnitude. The symbol for position is

dDirection can be given above or below the horizon, within a 2-D system (NEWS), or within a 3-D system (on Star Trek).

After the examples on the next slide complete the position worksheet.

For this class use the 2-D map system.

Record direction relative to north or south.

30.2o (measure)

15.41 cm (measure)

15.41 cm [N59.8oE]

11.6o (measure)

6.52 cm (measure)

6.52 cm [S11.6oW]

r.p.

DISPLACEMENT

Displacement is defined as change in position.

12 dddDisplacement is a vector with magnitude and direction. It is found in the difference between two position vectors. Take note that it is always final position minus initial position.

Displacement does not need a reference point. Displacement remains the same even if the reference point was changed.

...321

ddddRAnother equation for displacement is

25.31 cm (measure)

r.p.

24.5o (measure)

25.31 cm [S65.5oE]

initial point

final point

Try worksheet

Arrow points to final position!

Distance is defined as the length of path traveled. It is a scalar quantity and its symbol is

d

If you walked 10 m [E] then 10 m [W] then 10 m [N] your distance walked is 30 m while your displacement for the trip is 10 m [N].

Velocity and SpeedAre you moving?Can you feel movement?How do you know you are moving?

Velocity is defined as the change in position with respect to time. It is a vector quantity. t

dv

a vector divided by a scalar yields a vector

Speed is defined as distance traveled with respect to time. It is a scalar quantity. t

dv

Another equation for velocity is

t

dddv

...321

AccelerationAcceleration is defined as change in velocity with respect to time.

t

vva

12

t

va

In everyday usage acceleration often seems to mean speed up while decelerate means to slow down however technically this is not correct. Acceleration is a vector quantity therefore has magnitude and direction. In one-dimensional acceleration can have a positive or negative value. The sign indicates the sign of the velocity change since the change in time is always positive. Physicists do not mention deceleration. Speeding up refers to increasing magnitude of velocity while slowing down means the opposite.

Graphing

Graphs are often used in kinematics to represent position,velocity or acceleration (all versus time). Other quantities can be calculated from analysis of these graphs.

Curve SketchingDave begins west of the school and walks with a constant velocity and he passes the school. ([E] is positive)

t

d

This means position on a graph. We will never graph distance vs. time.

t

v

This means velocity on a graph. We will never graph speed vs. time.

Tanita walks back to school with a constant velocity, when she reaches the school she begins running with a constant velocity.

t

d

t

v

Karan runs away from school at a constant rate for a time then slows down until he stops.

t

d

t

v

t

a

A ball is thrown upwards and is caught below where it began.

t

d

t

v

t

a

Sketch a position vs. time graph, a velocity vs. time graph and an acceleration vs. time graph for the following situations.

a) A car travels forwards with a constant velocity of 50 km/hr [N].b) A person walks backwards with a velocity of 4 m/s [N].c) A person walks at 3 m/s for a period of time then jogs 6 m/s for the same period of time.d) A person walks at 3 m/s for a period of time then jogs home at 6 m/s in the opposite direction.e) A ball is thrown up out of a person’s hand; it rises and then returns to the person’s hand.

i) Sketch the graph for the velocity of the ball when it is out of the person’s hand.ii) Sketch the graph for the velocity of the ball for the complete

situation.f) A hockey puck slides along the smooth ice and bounces straight off the boards.g) A hockey puck is shot at a goalie and the goalie catches it.h) A person who slows down and speeds up without changing direction.i) A person who slows down and speeds up who does change direction. 

Constant Acceleration Kinematic Equations

Motion with a constant acceleration is an important type of motion which bears further analysis. In this unit only constant acceleration problems will be studied. The kinematic equations about to be shown or developed are only for constant acceleration!

The average velocity during a constant acceleration is found with this equation.

212

vv

vav tvv

d

)2

(12

So at this point when studying constant acceleration we have two equations.

t

vva

12 t

vvd

)2

(12

Constant Acceleration Kinematic Equations

The two constant acceleration equations below lead to 3 other kinematic equations.

tvv

d

)2

(12

t

vva

12

2

)2

2(

)2

(

)2

(

2

1

1

11

12

tatvd

tvta

d

tvvta

d

tvv

d

21

12

vvta

t

vva

davv 221

22

tavv 12 tvv

d

)2

( 12

21 2

ta

tvd

22 2

ta

tvd

ACCELERATION DUE TO GRAVITY

Objects that have a net force of gravity acting upon them experience an accel-eration due to gravity of 9.81 m/s2 [down].

g = 9.81 m/s2 [down]

In these situations the force of air resistance is ignored. (terminal velocity, coffee filter and motion sensor) This acceleration applies to objects going up or down (or both).

position

time

An object is thrown upwards and returns to the same height.

velocity

time

slope = - 9.81 m/s2

acceleration

time

- 9.81 m/s2

position

time

at max. height v = 0

these two t’s are equal

the velocity at this time is negative of the initial velocity

DOUBLE OBJECT PROBLEMS

-set up a direction system for each object such that each object moves in a positive direction

-there will always be a link between the two objects so that one variable can be eliminated

-extra information allows another equation to be written