Objectives• Describe motion in terms of displacement

and time.

• Calculate the displacement of an object

• Construct and interpret graphs of position versus time.

One Dimensional Motion

• To simplify the concept of motion, we will first consider motion that takes place in one direction.

• One example is the motion of a commuter train on a straight track.

Distance and Displacement

In physics we distinguish between the length of the trip (distance) and the direct distance between the starting point and ending point (displacement)

Distance – (scalar) – “how much ground an object has covered” during its motion

Displacement – (vector) – “how far out of place an object is”; it is the object’s change of position and its direction.

Distance

The length an object actually travels.

How far you go.

Scalar

Displacement

The change in position of an object.

Length between start and finish

Vector

Scalar– a quantity fully described by only a magnitude

• i.e. 5m; 20°C

Vector– a quantity fully described by both a magnitude

and direction.• i.e. 30 m/s, East; 5 mile, North

Displacement

• Displacement is a change in position.

• Displacement is not always equal to the distance traveled.

• The SI unit of displacement is the meter, m . . . Of course we know this

MotionExample:

A man walks 4m East, 2m South, 4m West and then 2m North.

2 m

4 m

2 m

4 m

Distance traveled = 12m

Displacement = 0m

Displacement

x = xf – xi displacement = final position – initial position

Displacement

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive or Negative Displacement?

Positive and Negative Displacements

Activity: Graphing Position vs. Time

To determine distance and displacement

Displacement

x = xf – xi displacement = final position – initial position

understanding the “distance – displacement" difference

Average Velocity

• Average velocity is the total displacement divided by the time interval during which the displacement occurred.

average velocity = change in position

change in time =

displacement

time interval

Average Velocity

f iavg

f i

x xxv

t t t

• In SI, the unit of velocity is meters per second, abbreviated as m/s.

Average Velocity

Velocity vs. Speed• Velocity describes motion with both a

direction and a numerical value (i.e. magnitude). (vector)

• Speed has no direction, only magnitude.

• Average speed is equal to the total distance traveled divided by the time interval. (scalar)

distance traveledaverage speed =

time of travel

Interpreting Velocity Graphically• For any position-time graph, we can determine

the average velocity by drawing a straight line between any two points on the graph.

• If the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity.

Interpreting Velocity Graphically

– Object 1: positive slope = positive velocity– Object 2: zero slope= zero velocity – Object 3: negative slope = negative velocity

Interpreting Velocity Graphically

The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.

The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.

Sign Conventions for Velocity

Constant VelocityThe fastest fish, the sailfish, can swim 1.2 × 102 km/h. Suppose you havea friend who lives on an island 16 km away from the shore. If you senda message using a sailfish as a messenger, how long will it take for themessage to reach your friend?

Constant Velocity

Use Dimensional Analysis!

The peregrine falcon is the fastest of flying birds (and, as a matter of fact, is the fastest living creature). A falcon can fly 1730 m downward in 25 s. What is the average velocity of a peregrine falcon?

In the Netherlands, there is an annual ice-skating race called the “Tour of the Eleven Towns.” The total distance of the course is 2.00 × 102 km, and the record time for covering it is 5 h and 40 min. Calculate the average speed of the record race in km/h.

The Sears Tower in Chicago is 443 m tall. Joe wants to set the world’s stair climbing record and runs all the way to the roof of the tower. If Joe’s average upward speed is 0.60 m/s, how long will it take Joe to climb from street level to the roof of the Sears Tower?