Displacement
There is a distinction between distance and displacement.
Displacement (blue line) is how far the object is from its starting point,
regardless of how it got there.
Distance traveled (dashed line) is measured along the actual path.
©2008 by W.H. Freeman
and Company
Displacement
The displacement is written:
Left:
Right:
Displacement is positive.
Displacement is negative.
©2008 by W.H. Freeman
and Company
Average Velocity
Speed: how far an object travels in a given time
interval
Velocity includes directional information:
x2  x1 x
v

t2  t1
t
©2008 by W.H. Freeman
and Company
A particle at t1 = -2.0 s is at x1= 3.4 cm and at t2 = 4.5 s is at x2= 8.5 cm.
What is its average velocity? Can you calculate its average speed from
these data?
The average velocity is given by
v 
x
t

8.5 cm  3.4 cm
4.5s   2.0 s 

5.1cm
6.5s
 0.78 cm s
The average speed cannot be calculated. To calculate the average speed, we would
need to know the actual distance traveled, and it is not given.
©2008 by W.H. Freeman
and Company
An airplane travels 3100 km at a speed of 790 km/h and then encounters a
tailwind that boosts its speed to 990 km/h for the next 2800 km. What was the
total time for the trip? What was the average speed of the plane for this trip?
The average speed for each segment of the trip is given by
v 
For the first segment,
d
t
t1 
For the second segment,
Thus the total time is
t 
, so
t2 
d1
v1
d2
v2


3100 km
790 km h
2800 km
d
v
for each segment.
 3.924 h
 2.828 h
990 km h
ttot  t1  t2  3.924 h  2.828 h  6.752 h  6.8 h
The average speed of the plane for the entire trip is
v 
©2008 by W.H. Freeman
and Company
d. tot
t tot

3100 km  2800 km
6.752 h
 873.8  8.7  10 km h
2