Distance and Displacement

Procedure•Draw a dot at the intersection of two lines

near the bottom edge of a sheet of graph paper. Label the dot “Start”.

•Draw a second, similar dot near the top of the paper. Label this dot “End”.

•Draw a path from the Start dot to the End dot. Choose any path that stays on the grid lines.

•Use a ruler to determine the distance of your path.

•This is the distance

Procedure 2

•Now draw a line directly from start to finish.

•Measure this distance with your ruler.•This is the displacement

Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

Example

Consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

Example

•Even though the physics teacher has walked a total distance of 12 meters, his displacement is 0 meters. During the course of motion, he has "covered 12 meters of ground" (distance = 12 m).

•Yet when he is finished walking, she is not "out of place" - i.e., there is no displacement for her motion (displacement = 0 m).

What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school?

The displacement of the runners is 0 miles. While they have covered a distance of 10 miles, they are not "out of place" or displaced. They finish where they started. Round-trip motions always have a displacement of 0.

What is the distance and the displacement of the race car drivers in the Daytona 500?

Distance: 500 milesDisplacement: 0

Scalar vs. Vector

•Scalars are quantities that are fully described by a magnitude (or numerical value) alone.

•Vectors are quantities that are fully described by both a magnitude and a direction.

Scalar or Vector?A. 5 m

B. 30 m/sec, East

C. 5 mi., North

D. 20 degrees Celsius

E. 256 bytes

F. 4000 Calories

Scalar or Vector?A. 5 m

▫ScalarB. 30 m/sec, East

▫VectorC. 5 mi., North

▫VectorD. 20 degrees Celsius

▫ScalarE. 256 bytes

▫ScalarF. 4000 Calories

▫Scalar

Displacement (x)

Straight line distance from the initial position to the final position (change in position)

Can be positive or negative

Displacement• What is the

displacement for the objects shown?

Displacement• What is the

displacement for the objects shown?

• Answer: 70 cm

• Answer: -60 cm

Algebra Review

3a + 8 = 32

a = 8

3c + 5 = 23

c = 6

d/4 + 8 = 16

d = 32

f = 45

f = 81

f + 36 = 117

f = 145.8